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Volumn 66, Issue 3, 2001, Pages 211-249

Wiener index of trees: Theory and applications

Author keywords

Distance (in a graph); Trees; Wiener index

Indexed keywords


EID: 0035329265     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010767517079     Document Type: Review
Times cited : (1210)

References (120)
  • 2
    • 0003146246 scopus 로고    scopus 로고
    • The graph theory approach to synthetic analysis: Definition and application of molecular complexity and synthetic complexity
    • Bertz, S. H. and Wright, W. F.: The graph theory approach to synthetic analysis: Definition and application of molecular complexity and synthetic complexity, Graph Theory Notes of New York 35 (1998), 32-48.
    • (1998) Graph Theory Notes of New York , vol.35 , pp. 32-48
    • Bertz, S.H.1    Wright, W.F.2
  • 3
    • 0009912199 scopus 로고
    • Parity of the distance numbers and Wiener numbers of bipartite graphs
    • Bonchev, D., Gutman, I. and Polansky, O. E.: Parity of the distance numbers and Wiener numbers of bipartite graphs, Comm. Math. Chem. (MATCH) 22 (1987), 209-214.
    • (1987) Comm. Math. Chem. (MATCH) , vol.22 , pp. 209-214
    • Bonchev, D.1    Gutman, I.2    Polansky, O.E.3
  • 4
    • 0343071989 scopus 로고
    • Information theory, distance matrix and molecular branching
    • Bonchev, D. and Trinajstić, N.: Information theory, distance matrix and molecular branching, J. Chem. Phys. 67 (1977), 4517-4533.
    • (1977) J. Chem. Phys. , vol.67 , pp. 4517-4533
    • Bonchev, D.1    Trinajstić, N.2
  • 5
    • 0000320758 scopus 로고
    • Mean distance in line graphs
    • Buckley, F.: Mean distance in line graphs, Congr. Numer. 32 (1981), 153-162.
    • (1981) Congr. Numer. , vol.32 , pp. 153-162
    • Buckley, F.1
  • 7
    • 0343280715 scopus 로고
    • Distance distributions and mean distance problem
    • C. C. Cadogan (ed.), University of the West Indies, Barbados
    • Buckley, F. and Superville, L.: Distance distributions and mean distance problem, In: C. C. Cadogan (ed.), Proc. Third Caribbean Conference on Combinatorics and Computing, University of the West Indies, Barbados, 1981, pp. 67-76.
    • (1981) Proc. Third Caribbean Conference on Combinatorics and Computing , pp. 67-76
    • Buckley, F.1    Superville, L.2
  • 9
    • 84988122955 scopus 로고
    • Determination of the Wiener molecular branching index for the general tree
    • Canfield, E. R., Robinson, R. W. and Rouvray, D. H.: Determination of the Wiener molecular branching index for the general tree, J. Comput. Chem. 6 (1985), 598-609.
    • (1985) J. Comput. Chem. , vol.6 , pp. 598-609
    • Canfield, E.R.1    Robinson, R.W.2    Rouvray, D.H.3
  • 11
    • 0001549507 scopus 로고
    • On the mathematical theory of isomers
    • Cayley, A.: On the mathematical theory of isomers, Phil. Magazine 47 (1874), 444-446.
    • (1874) Phil. Magazine , vol.47 , pp. 444-446
    • Cayley, A.1
  • 13
    • 0042797498 scopus 로고    scopus 로고
    • Wiener number as an immanant of the Laplacian of molecular graphs
    • Chan, O., Lam, T. K. and Merris, R.: Wiener number as an immanant of the Laplacian of molecular graphs, J. Chem. Inf. Comput. Sci. 37 (1997), 762-765.
    • (1997) J. Chem. Inf. Comput. Sci. , vol.37 , pp. 762-765
    • Chan, O.1    Lam, T.K.2    Merris, R.3
  • 14
    • 0031193219 scopus 로고    scopus 로고
    • The Wiener index and the Szeged index of benzenoid systems in linear time
    • Chepoi, V. and Klavžar, S.: The Wiener index and the Szeged index of benzenoid systems in linear time, J. Chem. Inf. Comput. Sci. 37 (1997), 752-755.
    • (1997) J. Chem. Inf. Comput. Sci. , vol.37 , pp. 752-755
    • Chepoi, V.1    Klavžar, S.2
  • 15
    • 0027814866 scopus 로고
    • Computing the average distance of an interval graph
    • Dankelmann, P.: Computing the average distance of an interval graph, Inform. Process. Lett. 48 (1993), 311-314.
    • (1993) Inform. Process. Lett. , vol.48 , pp. 311-314
    • Dankelmann, P.1
  • 16
    • 0009911881 scopus 로고
    • Average distance and independence number
    • Dankelmann, P.: Average distance and independence number, Discrete Appl. Math. 51 (1994), 75-83.
    • (1994) Discrete Appl. Math. , vol.51 , pp. 75-83
    • Dankelmann, P.1
  • 17
    • 0043245054 scopus 로고    scopus 로고
    • Average distance and domination number
    • Dankelmann, P.: Average distance and domination number, Discrete Appl. Math. 80 (1997), 21-35.
    • (1997) Discrete Appl. Math. , vol.80 , pp. 21-35
    • Dankelmann, P.1
  • 19
    • 0343716297 scopus 로고    scopus 로고
    • Average distance, minimum degree, and forbidden subgraphs
    • accepted for publication
    • Dankelmann, P. and Entringer, R.: Average distance, minimum degree, and forbidden subgraphs, J. Graph Theory (accepted for publication).
    • J. Graph Theory
    • Dankelmann, P.1    Entringer, R.2
  • 20
    • 0002236420 scopus 로고
    • Graph distance of catacondensed hexagonal polycyclic systems under its transformations
    • in Russian
    • Dobrynin, A. A.: Graph distance of catacondensed hexagonal polycyclic systems under its transformations, Vychisl. Sistemy 127 (1988), 3-39 (in Russian).
    • (1988) Vychisl. Sistemy , vol.127 , pp. 3-39
    • Dobrynin, A.A.1
  • 21
    • 0039076081 scopus 로고
    • Construction of graphs with a palindromic Wiener polynomial
    • in Russian
    • Dobrynin, A. A.: Construction of graphs with a palindromic Wiener polynomial, Vychisl. Sistemy 151 (1994), 37-54 (in Russian).
    • (1994) Vychisl. Sistemy , vol.151 , pp. 37-54
    • Dobrynin, A.A.1
  • 22
    • 0040854342 scopus 로고
    • Graphs with palindromic Wiener polynomials
    • Dobrynin, A. A.: Graphs with palindromic Wiener polynomials, Graph Theory Notes of New York 27 (1994), 50-54.
    • (1994) Graph Theory Notes of New York , vol.27 , pp. 50-54
    • Dobrynin, A.A.1
  • 24
    • 0346364234 scopus 로고    scopus 로고
    • Branchings in trees and the calculation of the Wiener index of a tree
    • Dobrynin, A. A.: Branchings in trees and the calculation of the Wiener index of a tree, Comm. Math. Chem. (MATCH) 41 (2000), 119-134.
    • (2000) Comm. Math. Chem. (MATCH) , vol.41 , pp. 119-134
    • Dobrynin, A.A.1
  • 25
    • 0001820677 scopus 로고
    • On a graph invariant related to the sum of all distances in a graph
    • Dobrynin, A. A. and Gutman, I.: On a graph invariant related to the sum of all distances in a graph, Publ. Inst. Math. (Beograd) 56 (1994), 18-22.
    • (1994) Publ. Inst. Math. (Beograd) , vol.56 , pp. 18-22
    • Dobrynin, A.A.1    Gutman, I.2
  • 26
    • 0009883799 scopus 로고    scopus 로고
    • The Wiener index for trees and graphs of hexagonal systems
    • in Russian
    • Dobrynin, A. A. and Gutman, I.: The Wiener index for trees and graphs of hexagonal systems, Diskret. Anal. Issled. Oper. Ser. 2 5(2) (1998), 34-60 (in Russian).
    • (1998) Diskret. Anal. Issled. Oper. Ser. 2 , vol.5 , Issue.2 , pp. 34-60
    • Dobrynin, A.A.1    Gutman, I.2
  • 27
    • 0342846051 scopus 로고    scopus 로고
    • Bicyclic graphs and their line graphs having the same Wiener index
    • in Russian
    • Dobrynin, A. A., Gutman, I. and Jovašević, V.: Bicyclic graphs and their line graphs having the same Wiener index, Diskret. Anal. Issled. Oper. Ser. 2 4(2) (1997), 3-9 (in Russian).
    • (1997) Diskret. Anal. Issled. Oper. Ser. 2 , vol.4 , Issue.2 , pp. 3-9
    • Dobrynin, A.A.1    Gutman, I.2    Jovašević, V.3
  • 28
    • 0342411069 scopus 로고
    • Metric invariants of subgraphs of molecular graphs
    • in Russian
    • Dobrynin, A. A. and Skorobogatov, V. A.: Metric invariants of subgraphs of molecular graphs, Vychisl. Sistemy 140 (1991), 3-61 (in Russian).
    • (1991) Vychisl. Sistemy , vol.140 , pp. 3-61
    • Dobrynin, A.A.1    Skorobogatov, V.A.2
  • 29
    • 49449129161 scopus 로고
    • Mean distance in a graph
    • Doyle, J. K. and Graver, J. E.: Mean distance in a graph, Discrete Math. 7 (1977), 147-154.
    • (1977) Discrete Math. , vol.7 , pp. 147-154
    • Doyle, J.K.1    Graver, J.E.2
  • 31
    • 0342411068 scopus 로고    scopus 로고
    • Bounds for the average distance-inverse degree product in trees
    • Y. Alavi, D. R. Lick and A. J. Schwenk (eds), New Issues Press, Kalamazoo
    • Entringer, R. C.: Bounds for the average distance-inverse degree product in trees, In: Y. Alavi, D. R. Lick and A. J. Schwenk (eds), Combinatorics, Graph Theory, and Algorithms, New Issues Press, Kalamazoo, 1999, pp. 335-352.
    • (1999) Combinatorics, Graph Theory, and Algorithms , pp. 335-352
    • Entringer, R.C.1
  • 35
    • 0000843813 scopus 로고    scopus 로고
    • Extension of edge connectivity index. Relationships to the line graph indices and QSPR applications
    • Estrada, E., Guevara, N. and Gutman, I.: Extension of edge connectivity index. Relationships to the line graph indices and QSPR applications, J. Chem. Inf. Comput. Sci. 38 (1998), 428-431.
    • (1998) J. Chem. Inf. Comput. Sci. , vol.38 , pp. 428-431
    • Estrada, E.1    Guevara, N.2    Gutman, I.3
  • 38
    • 85029423453 scopus 로고
    • A new characterization of tree medians with applications to distributed algorithms
    • Graph-Theoretic Concepts in Computer Science (Wiesbaden-Naurod, 1992), Springer, Berlin
    • Gerstel, O. and Zaks, S.: A new characterization of tree medians with applications to distributed algorithms, In: Graph-Theoretic Concepts in Computer Science (Wiesbaden-Naurod, 1992), Lecture Notes in Comput. Sci. 657, Springer, Berlin, 1993, pp. 135-144.
    • (1993) Lecture Notes in Comput. Sci. , vol.657 , pp. 135-144
    • Gerstel, O.1    Zaks, S.2
  • 39
    • 0343716295 scopus 로고
    • On the Wiener index of a graph
    • Graovac, A. and Pisanski, T.: On the Wiener index of a graph, J. Math. Chem. 8 (1991), 53-62.
    • (1991) J. Math. Chem. , vol.8 , pp. 53-62
    • Graovac, A.1    Pisanski, T.2
  • 40
    • 0342411066 scopus 로고
    • Independent vertex palindromic graphs
    • Gutman, I.: Independent vertex palindromic graphs, Graph Theory Notes of New York 23 (1992), 21-24.
    • (1992) Graph Theory Notes of New York , vol.23 , pp. 21-24
    • Gutman, I.1
  • 41
    • 0342411067 scopus 로고
    • A contribution to the study of palindromic graphs
    • Gutman, I.: A contribution to the study of palindromic graphs, Graph Theory Notes of New York 24 (1993), 51-56.
    • (1993) Graph Theory Notes of New York , vol.24 , pp. 51-56
    • Gutman, I.1
  • 42
    • 0001572481 scopus 로고
    • A new method for the calculation of the Wiener number of acyclic molecules
    • Gutman, I.: A new method for the calculation of the Wiener number of acyclic molecules, J. Mol. Struct. (Theochem) 285 (1993), 137-142.
    • (1993) J. Mol. Struct. (Theochem) , vol.285 , pp. 137-142
    • Gutman, I.1
  • 43
    • 21344481469 scopus 로고
    • Calculating the Wiener number: The Doyle-Graver method
    • Gutman, I.: Calculating the Wiener number: The Doyle-Graver method, J. Serb. Chem. Soc. 58 (1993), 745-750.
    • (1993) J. Serb. Chem. Soc. , vol.58 , pp. 745-750
    • Gutman, I.1
  • 44
    • 0040259875 scopus 로고
    • Some properties of the Wiener polynomial
    • Gutman, I.: Some properties of the Wiener polynomial, Graph Theory Notes of New York 25 (1993), 13-18.
    • (1993) Graph Theory Notes of New York , vol.25 , pp. 13-18
    • Gutman, I.1
  • 45
    • 0028464043 scopus 로고
    • Frequency of even and odd numbers in distance matrices of bipartite graphs
    • Gutman, I.: Frequency of even and odd numbers in distance matrices of bipartite graphs, J. Chem. Inf. Comput. Sci. 34 (1994), 912-914.
    • (1994) J. Chem. Inf. Comput. Sci. , vol.34 , pp. 912-914
    • Gutman, I.1
  • 46
    • 0028498920 scopus 로고
    • Selected properties of the Schultz molecular topological index
    • Gutman, I.: Selected properties of the Schultz molecular topological index, J. Chem. Inf. Comput. Sci. 34 (1994), 1087-1089.
    • (1994) J. Chem. Inf. Comput. Sci. , vol.34 , pp. 1087-1089
    • Gutman, I.1
  • 49
    • 2542583389 scopus 로고    scopus 로고
    • A property of the Wiener number and its modifications
    • Gutman, I.: A property of the Wiener number and its modifications, Indian J. Chem. 36A (1997), 128-132.
    • (1997) Indian J. Chem. , vol.36 A , pp. 128-132
    • Gutman, I.1
  • 50
    • 0032369488 scopus 로고    scopus 로고
    • Buckley-type relations for Wiener-type structure-descriptors
    • Gutman, I.: Buckley-type relations for Wiener-type structure-descriptors, J. Serb. Chem. Soc. 63 (1998), 487-492.
    • (1998) J. Serb. Chem. Soc. , vol.63 , pp. 487-492
    • Gutman, I.1
  • 51
  • 53
    • 0000028240 scopus 로고    scopus 로고
    • Topological indices based on the line graph of the molecular graph
    • Gutman, I. and Estrada, E.: Topological indices based on the line graph of the molecular graph, J. Chem. Inf. Comput. Sci. 36 (1996), 541-543.
    • (1996) J. Chem. Inf. Comput. Sci. , vol.36 , pp. 541-543
    • Gutman, I.1    Estrada, E.2
  • 55
    • 0342411065 scopus 로고    scopus 로고
    • Smallest graphs for which the distance of the graph is equal to the distance of its line graph
    • Gutman, I., Jovašević, V. and Dobrynin, A. A.: Smallest graphs for which the distance of the graph is equal to the distance of its line graph, Graph Theory Notes of New York 33 (1997), 19-19.
    • (1997) Graph Theory Notes of New York , vol.33 , pp. 19-19
    • Gutman, I.1    Jovašević, V.2    Dobrynin, A.A.3
  • 56
    • 0001038633 scopus 로고
    • Chemical applications of the Laplacian spectrum of molecular graphs: Studies of the Wiener number
    • Gutman, I., Lee, S. L., Chu, C. H. and Luo, Y. L.: Chemical applications of the Laplacian spectrum of molecular graphs: studies of the Wiener number, Indian J. Chem. 33A (1994), 603-608.
    • (1994) Indian J. Chem. , vol.33 A , pp. 603-608
    • Gutman, I.1    Lee, S.L.2    Chu, C.H.3    Luo, Y.L.4
  • 57
    • 0001112105 scopus 로고    scopus 로고
    • Trees with extremal hyper-Wiener index: Mathematical basis and chemical applications
    • Gutman, I., Linert, W., Lukovits, I. and Dobrynin, A. A.: Trees with extremal hyper-Wiener index: Mathematical basis and chemical applications, J. Chem. Inf. Comput. Sci. 37 (1997), 349-354.
    • (1997) J. Chem. Inf. Comput. Sci. , vol.37 , pp. 349-354
    • Gutman, I.1    Linert, W.2    Lukovits, I.3    Dobrynin, A.A.4
  • 59
    • 84986430578 scopus 로고
    • The mean isomer degeneracy of the Wiener index
    • Gutman, I., Luo, Y. L. and Lee, S. L.: The mean isomer degeneracy of the Wiener index, J. Chin. Chem. Soc. 40 (1993), 195-198.
    • (1993) J. Chin. Chem. Soc. , vol.40 , pp. 195-198
    • Gutman, I.1    Luo, Y.L.2    Lee, S.L.3
  • 60
    • 21844525007 scopus 로고
    • Correlation between Wiener and quasi-Wiener indices in benzenoid hydrocarbons
    • Gutman, I., Marković, S. and Bančević, Ž.: Correlation between Wiener and quasi-Wiener indices in benzenoid hydrocarbons, J. Serb. Chem. Soc. 60 (1995), 633-636.
    • (1995) J. Serb. Chem. Soc. , vol.60 , pp. 633-636
    • Gutman, I.1    Marković, S.2    Bančević, Ž.3
  • 61
    • 0010401244 scopus 로고    scopus 로고
    • The quasi-Wiener and the Kirchhoff indices coincide
    • Gutman, I. and Mohar, B.: The quasi-Wiener and the Kirchhoff indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996), 982-985.
    • (1996) J. Chem. Inf. Comput. Sci. , vol.36 , pp. 982-985
    • Gutman, I.1    Mohar, B.2
  • 64
    • 30244524022 scopus 로고    scopus 로고
    • Wiener index and intermolecular forces
    • Gutman, I. and Potgieter, J. H.: Wiener index and intermolecular forces, J. Serb. Chem. Soc. 62 (1997), 185-192.
    • (1997) J. Serb. Chem. Soc. , vol.62 , pp. 185-192
    • Gutman, I.1    Potgieter, J.H.2
  • 65
    • 0042007855 scopus 로고
    • A new theorem for the Wiener molecular branching index of trees with perfect matchings
    • Gutman, I. and Rouvray, D. H.: A new theorem for the Wiener molecular branching index of trees with perfect matchings, Comput. Chem. 14 (1990), 29-32.
    • (1990) Comput. Chem. , vol.14 , pp. 29-32
    • Gutman, I.1    Rouvray, D.H.2
  • 66
    • 0001636128 scopus 로고
    • The range of the Wiener index and mean isomer degeneracy
    • Gutman, I. and Šoltés, L.: The range of the Wiener index and mean isomer degeneracy, Z Naturforsch. 46A (1991), 865-868.
    • (1991) Z Naturforsch. , vol.46 A , pp. 865-868
    • Gutman, I.1    Šoltés, L.2
  • 67
    • 33751133441 scopus 로고    scopus 로고
    • On graph representation of organic molecules -Cayley's plerograms vs. his kenograms
    • Gutman, I., Vidović, D. and Popović, L.: On graph representation of organic molecules -Cayley's plerograms vs. his kenograms, J. Chem. Soc. Faraday Trans. 94 (1998), 857-860.
    • (1998) J. Chem. Soc. Faraday Trans. , vol.94 , pp. 857-860
    • Gutman, I.1    Vidović, D.2    Popović, L.3
  • 68
    • 0009941674 scopus 로고
    • The sum of all distances in bipartite graphs
    • Gutman, I. and Yeh, Y. N.: The sum of all distances in bipartite graphs, Math. Slovaca 45 (1995), 327-334.
    • (1995) Math. Slovaca , vol.45 , pp. 327-334
    • Gutman, I.1    Yeh, Y.N.2
  • 70
    • 0000958261 scopus 로고
    • Some recent results in the theory of the Wiener number
    • Gutman, I., Yeh, Y. N., Lee, S. L. and Luo, Y. L.: Some recent results in the theory of the Wiener number, Indian J. Chem. 32A (1993), 651-661.
    • (1993) Indian J. Chem. , vol.32 A , pp. 651-661
    • Gutman, I.1    Yeh, Y.N.2    Lee, S.L.3    Luo, Y.L.4
  • 71
    • 0040558669 scopus 로고
    • The number of caterpillars
    • Harary, F. and Schwenk, A. J.: The number of caterpillars, Discrete Math. 6 (1973), 359-365.
    • (1973) Discrete Math. , vol.6 , pp. 359-365
    • Harary, F.1    Schwenk, A.J.2
  • 72
    • 84987045114 scopus 로고
    • On mean distance in certain classes of graphs
    • Hendry, G. R. T.: On mean distance in certain classes of graphs, Networks 19 (1989), 451-457.
    • (1989) Networks , vol.19 , pp. 451-457
    • Hendry, G.R.T.1
  • 73
    • 0001219776 scopus 로고
    • Topological index. a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons
    • Hosoya, H.: Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 4 (1971), 2332-2339.
    • (1971) Bull. Chem. Soc. Jpn. , vol.4 , pp. 2332-2339
    • Hosoya, H.1
  • 74
    • 0023980693 scopus 로고
    • On some counting polynomials in chemistry
    • Hosoya, H.: On some counting polynomials in chemistry, Discrete Appl. Math. 19 (1988), 239-257.
    • (1988) Discrete Appl. Math. , vol.19 , pp. 239-257
    • Hosoya, H.1
  • 75
    • 0000602164 scopus 로고
    • Optimum communication spanning trees
    • Hu, T. C.: Optimum communication spanning trees, SIAM J. Comput. 3 (1974), 188-195.
    • (1974) SIAM J. Comput. , vol.3 , pp. 188-195
    • Hu, T.C.1
  • 76
    • 0010760125 scopus 로고
    • Die Berechnung des Wiener Index für einfache Polybäume
    • John, P. E.: Die Berechnung des Wiener Index für einfache Polybäume, Comm. Math. Chem. (MATCH) 31 (1994), 123-132.
    • (1994) Comm. Math. Chem. (MATCH) , vol.31 , pp. 123-132
    • John, P.E.1
  • 77
    • 84986976912 scopus 로고
    • The complexity of the network design problem
    • Johnson, D. S., Lenstra, J. K. and Rinnooy-Kan, A. H. G.: The complexity of the network design problem, Networks 8 (1978), 279-285.
    • (1978) Networks , vol.8 , pp. 279-285
    • Johnson, D.S.1    Lenstra, J.K.2    Rinnooy-Kan, A.H.G.3
  • 78
    • 84942401057 scopus 로고
    • Sur les assemblages de lignes
    • Jordan, C.: Sur les assemblages de lignes, J. Reine Angew. Math. 70 (1869), 185-190.
    • (1869) J. Reine Angew. Math. , vol.70 , pp. 185-190
    • Jordan, C.1
  • 80
  • 82
    • 33751156681 scopus 로고
    • Labeling of benzenoid systems which reflects the vertex-distance relations
    • Klavžar, S., Gutman, I. and Mohar, B.: Labeling of benzenoid systems which reflects the vertex-distance relations, J. Chem. Inf. Comput. Sci. 35 (1995), 590-593.
    • (1995) J. Chem. Inf. Comput. Sci. , vol.35 , pp. 590-593
    • Klavžar, S.1    Gutman, I.2    Mohar, B.3
  • 83
    • 0009883801 scopus 로고    scopus 로고
    • Algebraic approach to fasciagraphs and rotagraphs
    • Klavžar, S. and Žerovnik, J.: Algebraic approach to fasciagraphs and rotagraphs, Discrete Appl. Math. 68 (1996), 93-100.
    • (1996) Discrete Appl. Math. , vol.68 , pp. 93-100
    • Klavžar, S.1    Žerovnik, J.2
  • 87
    • 0001044268 scopus 로고    scopus 로고
    • A collective property of trees and chemical trees
    • Lepović, M. and Gutman, I.: A collective property of trees and chemical trees, J. Chem. Inf. Comput. Sci. 38 (1998), 823-826.
    • (1998) J. Chem. Inf. Comput. Sci. , vol.38 , pp. 823-826
    • Lepović, M.1    Gutman, I.2
  • 88
    • 0001919145 scopus 로고
    • General formulas for the Wiener index
    • Lukovits, I.: General formulas for the Wiener index, J. Chem. Inf. Comput. Sci. 31 (1991), 503-507.
    • (1991) J. Chem. Inf. Comput. Sci. , vol.31 , pp. 503-507
    • Lukovits, I.1
  • 89
    • 0342411061 scopus 로고
    • Frequency of even and odd numbers in distance matrices of trees
    • Lukovits, I.: Frequency of even and odd numbers in distance matrices of trees, J. Chem. Inf. Comput. Sci. 33 (1993), 626-629.
    • (1993) J. Chem. Inf. Comput. Sci. , vol.33 , pp. 626-629
    • Lukovits, I.1
  • 90
    • 0342846048 scopus 로고    scopus 로고
    • Personal communication
    • McCanna, J. E.: Personal communication.
    • McCanna, J.E.1
  • 91
    • 0342411060 scopus 로고
    • Topological indices for molecular fragments
    • Mekenyan, O., Bonchev, D. and Balaban, A. T.: Topological indices for molecular fragments, J. Math. Chem. 2 (1988), 347-375.
    • (1988) J. Math. Chem. , vol.2 , pp. 347-375
    • Mekenyan, O.1    Bonchev, D.2    Balaban, A.T.3
  • 92
    • 0000029225 scopus 로고
    • Graph-theoretical approach to the calculation of phsysico-chemical properties of polymers
    • Mekenyan, O., Dimitrov, S. and Bonchev, D.: Graph-theoretical approach to the calculation of phsysico-chemical properties of polymers, Eur. Polym. J. 19 (1983), 1185-1193.
    • (1983) Eur. Polym. J. , vol.19 , pp. 1185-1193
    • Mekenyan, O.1    Dimitrov, S.2    Bonchev, D.3
  • 93
    • 0010677524 scopus 로고
    • An edge version of the matrix-tree theorem and the Wiener index
    • Merris, R.: An edge version of the matrix-tree theorem and the Wiener index, Linear and Multilinear Algebra 25 (1989), 291-296.
    • (1989) Linear and Multilinear Algebra , vol.25 , pp. 291-296
    • Merris, R.1
  • 94
    • 84986514804 scopus 로고
    • The distance spectrum of a tree
    • Merris, R.: The distance spectrum of a tree, J. Graph Theory 14 (1990), 365-369.
    • (1990) J. Graph Theory , vol.14 , pp. 365-369
    • Merris, R.1
  • 95
    • 33750999449 scopus 로고
    • Laplacian matrices of graphs: A survey
    • Merris, R.: Laplacian matrices of graphs: A survey, Linear Algebra Appl. 197/198 (1994), 143-176.
    • (1994) Linear Algebra Appl. , vol.197-198 , pp. 143-176
    • Merris, R.1
  • 96
    • 0001216057 scopus 로고
    • The Laplacian spectrum of graphs
    • Y. Alavi, G. Chartrand, O. R. Ollermann and A. J. Schwenk (eds), Wiley, New York
    • Mohar, B.: The Laplacian spectrum of graphs, In: Y. Alavi, G. Chartrand, O. R. Ollermann and A. J. Schwenk (eds), Graph Theory, Combinatorics, and Applications, Wiley, New York, 1991, pp. 871-898.
    • (1991) Graph Theory, Combinatorics, and Applications , pp. 871-898
    • Mohar, B.1
  • 97
    • 0002427040 scopus 로고
    • Eigenvalues, diameter, and mean distance in graphs
    • Mohar, B.: Eigenvalues, diameter, and mean distance in graphs, Graphs Combin. 7 (1991), 53-64.
    • (1991) Graphs Combin. , vol.7 , pp. 53-64
    • Mohar, B.1
  • 99
    • 0000024686 scopus 로고
    • How to compute the Wiener index of a graph
    • Mohar, B. and Pisanski, T.: How to compute the Wiener index of a graph, J. Math. Chem. 2 (1988), 267-277.
    • (1988) J. Math. Chem. , vol.2 , pp. 267-277
    • Mohar, B.1    Pisanski, T.2
  • 100
    • 0343280705 scopus 로고    scopus 로고
    • On the total distance between nodes in trees
    • Moon, J. W.: On the total distance between nodes in trees, Systems Sci. Math. Sci. 9 (1996), 93-96.
    • (1996) Systems Sci. Math. Sci. , vol.9 , pp. 93-96
    • Moon, J.W.1
  • 101
  • 102
    • 84986439448 scopus 로고
    • On the sum of all distances in a graph or digraph
    • Plesnik, J.: On the sum of all distances in a graph or digraph, J. Graph Theory 8 (1984), 1-21.
    • (1984) J. Graph Theory , vol.8 , pp. 1-21
    • Plesnik, J.1
  • 103
    • 0000152720 scopus 로고
    • The Wiener number of graphs. I. General theory and changes due to some graph operations
    • Polansky, O. E. and Bonchev, D.: The Wiener number of graphs. I. General theory and changes due to some graph operations, Comm. Math. Chem. (MATCH) 21 (1986), 133-186.
    • (1986) Comm. Math. Chem. (MATCH) , vol.21 , pp. 133-186
    • Polansky, O.E.1    Bonchev, D.2
  • 104
    • 0002402010 scopus 로고
    • Theory of the Wiener number of graphs. II. Transfer graphs and some of their metric properties
    • Polansky, O. E. and Bonchev, D.: Theory of the Wiener number of graphs. II. Transfer graphs and some of their metric properties, Comm. Math. Chem. (MATCH) 25 (1990), 3-39.
    • (1990) Comm. Math. Chem. (MATCH) , vol.25 , pp. 3-39
    • Polansky, O.E.1    Bonchev, D.2
  • 105
    • 51649146515 scopus 로고
    • Kombinatorische Anzahlbestimmungen für Gruppen, Graphen and chemische Verbindungen
    • sections 35-37, 55
    • Pólya, G.: Kombinatorische Anzahlbestimmungen für Gruppen, Graphen and chemische Verbindungen, Acta Math. 68 (1937), 145-254, sections 35-37, 55.
    • (1937) Acta Math. , vol.68 , pp. 145-254
    • Pólya, G.1
  • 106
    • 0032222117 scopus 로고    scopus 로고
    • A bound involving the centroid and Wiener index of a tree
    • Porter, T. D.: A bound involving the centroid and Wiener index of a tree, Utilitas Math. 53 (1998), 141-146.
    • (1998) Utilitas Math. , vol.53 , pp. 141-146
    • Porter, T.D.1
  • 107
    • 0022013813 scopus 로고
    • Structural selectivity of topological indexes in alkane series
    • Razinger, M., Chretien, J. R. and Dubois, J.: Structural selectivity of topological indexes in alkane series, J. Chem. Inf. Comput. Sci. 25 (1985), 23-27.
    • (1985) J. Chem. Inf. Comput. Sci. , vol.25 , pp. 23-27
    • Razinger, M.1    Chretien, J.R.2    Dubois, J.3
  • 108
    • 0000059848 scopus 로고
    • Should we have designs on topological indices?
    • R. B. King (ed.), Elsevier, Amsterdam
    • Rouvray, D. H.: Should we have designs on topological indices?, In: R. B. King (ed.), Chemical Application of Topology and Graph Theory, Elsevier, Amsterdam, 1983, pp. 159-177.
    • (1983) Chemical Application of Topology and Graph Theory , pp. 159-177
    • Rouvray, D.H.1
  • 109
    • 0022775421 scopus 로고
    • Predicting chemistry from topology
    • Rouvray, D. H.: Predicting chemistry from topology, Sci. Amer. 255(9) (1986), 40-47.
    • (1986) Sci. Amer. , vol.255 , Issue.9 , pp. 40-47
    • Rouvray, D.H.1
  • 110
    • 84988084545 scopus 로고
    • The modelling of chemical phenomena using topological indices
    • Rouvray, D. H.: The modelling of chemical phenomena using topological indices, J. Comput. Chem. 8 (1987), 470-480.
    • (1987) J. Comput. Chem. , vol.8 , pp. 470-480
    • Rouvray, D.H.1
  • 111
    • 0342846044 scopus 로고
    • The average distance of trees
    • Shi, R.: The average distance of trees, Systems Sci. Math. Sci. 6 (1993), 18-24.
    • (1993) Systems Sci. Math. Sci. , vol.6 , pp. 18-24
    • Shi, R.1
  • 112
    • 0342411059 scopus 로고
    • Influence of the structural transformations of a graph on its distance
    • in Russian
    • Skorobogatov, V. A. and Dobrynin, A. A.: Influence of the structural transformations of a graph on its distance, Vychisl. Sistemy 117 (1986), 103-113 (in Russian).
    • (1986) Vychisl. Sistemy , vol.117 , pp. 103-113
    • Skorobogatov, V.A.1    Dobrynin, A.A.2
  • 114
    • 0039748558 scopus 로고
    • Transmission in graphs: A bound and vertex removing
    • Šoltés, L.: Transmission in graphs: A bound and vertex removing, Math. Slovaca 41 (1991), 11-16.
    • (1991) Math. Slovaca , vol.41 , pp. 11-16
    • Šoltés, L.1
  • 116
    • 8544254107 scopus 로고
    • Structural determination of paraffin boiling points
    • Wiener, H.: Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947), 17-20.
    • (1947) J. Amer. Chem. Soc. , vol.69 , pp. 17-20
    • Wiener, H.1
  • 117
    • 0342846041 scopus 로고
    • Mean distance in a tree
    • Winkler, P.: Mean distance in a tree, Discrete Appl. Math. 27 (1990), 179-185.
    • (1990) Discrete Appl. Math. , vol.27 , pp. 179-185
    • Winkler, P.1
  • 118
    • 43949155539 scopus 로고
    • On the sum of all distances in composite graphs
    • Yeh, Y. N. and Gutman, I.: On the sum of all distances in composite graphs, Discrete Math. 135 (1994), 359-365.
    • (1994) Discrete Math. , vol.135 , pp. 359-365
    • Yeh, Y.N.1    Gutman, I.2
  • 119
    • 0002750931 scopus 로고
    • Medians and peripherians of trees
    • Zelinka, B.: Medians and peripherians of trees, Arch. Math. (Brno) 4 (1968), 87-95.
    • (1968) Arch. Math. (Brno) , vol.4 , pp. 87-95
    • Zelinka, B.1


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