메뉴 건너뛰기




Volumn 65, Issue 3, 2011, Pages 595-644

Survey on geometric-arithmetic indices of graphs

Author keywords

[No Author keywords available]

Indexed keywords


EID: 80051538005     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review
Times cited : (153)

References (96)
  • 1
  • 3
    • 43949120798 scopus 로고    scopus 로고
    • PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers
    • A. R. Ashrafi, M. Mirzagar, PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers, Indian J. Chem. 47A (2008) 538-541.
    • (2008) Indian J. Chem. , vol.47 , pp. 538-541
    • Ashrafi, A.R.1    Mirzagar, M.2
  • 7
    • 77955697769 scopus 로고    scopus 로고
    • The geometric-arithemtic index of nanotubes
    • S. Chen, W. Liu, the geometric-arithemtic index of nanotubes, J. Comput. Theor. Nanosci. 7 (2010) 1993-1995.
    • (2010) J. Comput. Theor. Nanosci. , vol.7 , pp. 1993-1995
    • Chen, S.1    Liu, W.2
  • 8
    • 67651160482 scopus 로고    scopus 로고
    • Maximum values of Szeged index and edge-Szeged index of graphs
    • E. Chiniforooshan, B. Wu, Maximum values of Szeged index and edge-Szeged index of graphs, El. Notes Discr. Math. 34 (2009) 405-409.
    • (2009) El. Notes Discr. Math. , vol.34 , pp. 405-409
    • Chiniforooshan, E.1    Wu, B.2
  • 10
    • 77951143115 scopus 로고    scopus 로고
    • On comparing Zagreb indices of graphs
    • K. C. Das, On comparing Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 63 (2010) 433-440.
    • (2010) MATCH Commun. Math. Comput. Chem. , vol.63 , pp. 433-440
    • Das, K.C.1
  • 11
    • 77957550545 scopus 로고    scopus 로고
    • On geometric-arithmetic index of graphs
    • K. C. Das, On geometric-arithmetic index of graphs, MATCH Commun. Math. Comput. Chem. 64 (2010) 619-630.
    • (2010) MATCH Commun. Math. Comput. Chem. , vol.64 , pp. 619-630
    • Das, K.C.1
  • 12
    • 79952473903 scopus 로고    scopus 로고
    • Estimating the Wiener index by means of number of vertices, number of edges, and diameter
    • K. C. Das, I. Gutman, Estimating the Wiener index by means of number of vertices, number of edges, and diameter, MATCH Commun. Math. Comput. Chem. 64 (2010) 647-660.
    • (2010) MATCH Commun. Math. Comput. Chem. , vol.64 , pp. 647-660
    • Das, K.C.1    Gutman, I.2
  • 16
    • 77957561568 scopus 로고    scopus 로고
    • Comparison between first geometric-arithmetic index and atom-bond connectivity index
    • K. C. Das, N. Trinajstić, Comparison between first geometric-arithmetic index and atom-bond connectivity index, Chem. Phys. Lett. 497 (2010) 149-151.
    • (2010) Chem. Phys. Lett. , vol.497 , pp. 149-151
    • Das, K.C.1    Trinajstić, N.2
  • 22
    • 72149099348 scopus 로고    scopus 로고
    • On Randić indices of chemical trees and chemical unicyclic graphs
    • Z. Du, B. Zhou, N. Trinajstić, On Randić indices of chemical trees and chemical unicyclic graphs, MATCH Commun. Math. Comput. Chem. 62 (2009) 131-142.
    • (2009) MATCH Commun. Math. Comput. Chem. , vol.62 , pp. 131-142
    • Du, Z.1    Zhou, B.2    Trinajstić, N.3
  • 23
    • 0000280492 scopus 로고    scopus 로고
    • Characterization of 3D molecular structure
    • E. Estrada, Characterization of 3D molecular structure, Chem. Phys. Lett. 319 (2000) 713-718.
    • (2000) Chem. Phys. Lett. , vol.319 , pp. 713-718
    • Estrada, E.1
  • 27
    • 42249099257 scopus 로고    scopus 로고
    • Energy and Estrada index of phenylenes
    • B. Furtula, I. Gutman, Energy and Estrada index of phenylenes, Indian J. Chem. 47A (2008) 220-224.
    • (2008) Indian J. Chem. , vol.47 A , pp. 220-224
    • Furtula, B.1    Gutman, I.2
  • 28
    • 79953186020 scopus 로고    scopus 로고
    • Relation between second and third geometric-arithmetic indices of trees
    • in press
    • B. Furtula, I. Gutman, Relation between second and third geometric-arithmetic indices of trees, J. Chemometrics, in press.
    • J. Chemometrics
    • Furtula, B.1    Gutman, I.2
  • 30
    • 70449119195 scopus 로고    scopus 로고
    • Computing a new topological index of nano structures
    • M. Ghorbani, M. Jalali, Computing a new topological index of nano structures, Dig. J. Nanomater. Bios. 4 (2009) 681-685.
    • (2009) Dig. J. Nanomater. Bios. , vol.4 , pp. 681-685
    • Ghorbani, M.1    Jalali, M.2
  • 32
    • 0000177681 scopus 로고
    • Easy method for the calculation of the algebraic structure count of phenylenes
    • I. Gutman, Easy method for the calculation of the algebraic structure count of phenylenes, J. Chem. Soc. Faraday Trans. 89 (1993) 2413-2416.
    • (1993) J. Chem. Soc. Faraday Trans. , vol.89 , pp. 2413-2416
    • Gutman, I.1
  • 33
    • 0002345564 scopus 로고
    • A formula for the Wiener number of trees and its extension to graphs containing cycles
    • I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes New York 27 (1994) 9-15.
    • (1994) Graph Theory Notes New York , vol.27 , pp. 9-15
    • Gutman, I.1
  • 34
    • 0001942953 scopus 로고
    • A regularity for the total π-electron energy of phenylenes
    • I. Gutman, A regularity for the total π-electron energy of phenylenes, MATCH Commun. Math. Chem. 31 (1994) 99-110.
    • (1994) MATCH Commun. Math. Chem. , vol.31 , pp. 99-110
    • Gutman, I.1
  • 35
    • 0011983412 scopus 로고    scopus 로고
    • The energy of a graph: Old and new results
    • A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.), Springer-Verlag, Berlin
    • I. Gutman, The energy of a graph: Old and new results, in: A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer-Verlag, Berlin, 2001, pp. 196-211.
    • (2001) Algebraic Combinatorics and Applications , pp. 196-211
    • Gutman, I.1
  • 36
    • 55249113026 scopus 로고    scopus 로고
    • The edge version of the Szeged index
    • I. Gutman, A. R. Ashrafi, The edge version of the Szeged index, Croat. Chem. Acta (2008) 263-266.
    • (2008) Croat. Chem. Acta , pp. 263-266
    • Gutman, I.1    Ashrafi, A.R.2
  • 38
    • 21844526556 scopus 로고
    • Enumeration of the isomers of phenylenes
    • I. Gutman, S. J. Cyvin, J. Brunvoll, Enumeration of the isomers of phenylenes, Monatsh. Chem. 125 (1994) 887-894.
    • (1994) Monatsh. Chem. , vol.125 , pp. 887-894
    • Gutman, I.1    Cyvin, S.J.2    Brunvoll, J.3
  • 44
    • 85076583537 scopus 로고    scopus 로고
    • Estimating the second and third geometric-arithmetic indices
    • in press
    • I. Gutman, B. Furtula, Estimating the second and third geometric-arithmetic indices, Haccettepe J. Math. Stat., in press.
    • Haccettepe J. Math. Stat.
    • Gutman, I.1    Furtula, B.2
  • 45
    • 33749273283 scopus 로고    scopus 로고
    • Relations between Wiener numbers of benzenoid hydrocarbons and phenylenes
    • I. Gutman, S. Klavžar, Relations between Wiener numbers of benzenoid hydrocarbons and phenylenes, ACH - Models Chem. 135 (1998) 45-55. (Pubitemid 128771625)
    • (1998) ACH - Models in Chemistry , vol.135 , Issue.1-2 , pp. 45-55
    • Gutman, I.1    Klavzar, S.2
  • 47
  • 49
    • 33845352210 scopus 로고
    • Graph theory and molecular orbitais. Total π-electron energy of alternant hydrocarbons
    • I. Gutman, N. Trinajstić, Graph theory and molecular orbitais. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535-538.
    • (1972) Chem. Phys. Lett. , vol.17 , pp. 535-538
    • Gutman, I.1    Trinajstić, N.2
  • 53
    • 0001219776 scopus 로고    scopus 로고
    • Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons
    • H. Hosoya, Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Japan 44 2332-2339.
    • Bull. Chem. Soc. Japan , vol.44 , pp. 2332-2339
    • Hosoya, H.1
  • 55
    • 79951887224 scopus 로고    scopus 로고
    • Trees with given diameter and minimum second geometric-arithmetic index
    • H. Hua, Trees with given diameter and minimum second geometric-arithmetic index, MATCH Commun. Math. Comput. Chem. 64 (2010) 631-638.
    • (2010) MATCH Commun. Math. Comput. Chem. , vol.64 , pp. 631-638
    • Hua, H.1
  • 56
    • 79955557492 scopus 로고    scopus 로고
    • A unified approach to extremal trees with respect to geometric- arithemtic, Szeged and edge Szeged indices
    • in press
    • H. Hua, S. Zhang, A unified approach to extremal trees with respect to geometric-arithemtic, Szeged and edge Szeged indices, MATCH Commun. Math. Comput. Chem. 65 (2011), in press.
    • (2011) MATCH Commun. Math. Comput. Chem. , vol.65
    • Hua, H.1    Zhang, S.2
  • 57
    • 0342819025 scopus 로고
    • Helical microtubules of graphitic carbon
    • S. Iijima, Helical microtubules of graphitic carbon, Nature 354 (1991) 56-58. (Pubitemid 21896780)
    • (1991) Nature , vol.354 , Issue.6348 , pp. 56-58
    • Iijima, S.1
  • 60
    • 0001623253 scopus 로고    scopus 로고
    • On a novel structural descriptor PI
    • P. V. Khadikar, On a novel structural descriptor PI, Nat. Acad. Sci. Lett. 23 (2000) 113-118.
    • (2000) Nat. Acad. Sci. Lett. , vol.23 , pp. 113-118
    • Khadikar, P.V.1
  • 61
    • 52149086974 scopus 로고    scopus 로고
    • A matrix method for computing Szeged and vertex PI indices of join and composition of graph
    • M. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, A matrix method for computing Szeged and vertex PI indices of join and composition of graph, Lin. Algebra Appl. 429 (2008) 2702-2709.
    • (2008) Lin. Algebra Appl. , vol.429 , pp. 2702-2709
    • Khalifeh, M.H.1    Yousefi-Azari, H.2    Ashrafi, A.R.3
  • 62
    • 45849098000 scopus 로고    scopus 로고
    • Vertex and edge PI indices of Cartesian product of graphs
    • M. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, Vertex and edge PI indices of Cartesian product of graphs, Discr. Appl. Math. 156 (2008) 1780-1789.
    • (2008) Discr. Appl. Math. , vol.156 , pp. 1780-1789
    • Khalifeh, M.1    Yousefi-Azari, H.2    Ashrafi, A.R.3
  • 66
    • 63049086508 scopus 로고    scopus 로고
    • On minimal energy and Hosoya index of unicyclic graphs
    • S. Li, X. Li, Z. Zhu, On minimal energy and Hosoya index of unicyclic graphs, MATCH Commun. Math. Comput. Chem. 61 (2009) 325-339.
    • (2009) MATCH Commun. Math. Comput. Chem. , vol.61 , pp. 325-339
    • Li, S.1    Li, X.2    Zhu, Z.3
  • 69
    • 77951108772 scopus 로고    scopus 로고
    • A simple approach to order the first Zagreb indices of connected graphs
    • M. Liu, A simple approach to order the first Zagreb indices of connected graphs, MATCH Commun. Math. Comput. Chem. 63 (2010) 425-432.
    • (2010) MATCH Commun. Math. Comput. Chem. , vol.63 , pp. 425-432
    • Liu, M.1
  • 71
    • 61849113350 scopus 로고    scopus 로고
    • The vertex PI index and Szeged index of bridge graphs
    • T. Mansour, M. Schork, The vertex PI index and Szeged index of bridge graphs, Discr. Appl. Math. 157 (2009) 1600-1606.
    • (2009) Discr. Appl. Math. , vol.157 , pp. 1600-1606
    • Mansour, T.1    Schork, M.2
  • 78
    • 0000152515 scopus 로고    scopus 로고
    • Randić index of benzenoid systems and phenylenes
    • J. Rada, O. Araújo, I. Gutman, Randić index of benzenoid systems and phenylenes, Croat. Chem. Acta 74 (2001) 225-235. (Pubitemid 33614359)
    • (2001) Croatica Chemica Acta , vol.74 , Issue.2 , pp. 225-235
    • Rada, J.1    Araujo, O.2    Gutman, I.3
  • 79
    • 8644280181 scopus 로고
    • On characterization of molecular branching
    • M. Randić, On characterization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609-6615.
    • (1975) J. Am. Chem. Soc. , vol.97 , pp. 6609-6615
    • Randić, M.1
  • 80
    • 79955559408 scopus 로고    scopus 로고
    • Note on the second geometric-arithmetic index
    • in press
    • Z. Tang, Y. Hou, Note on the second geometric-arithmetic index, MATCH Commun. Math. Comput. Chem. 65 (2011), in press.
    • (2011) MATCH Commun. Math. Comput. Chem. , vol.65
    • Tang, Z.1    Hou, Y.2
  • 82
    • 80051502211 scopus 로고    scopus 로고
    • TRC Thermodynamic Tables - Hydrocarbons; Thermodynamic Research Center, The Texas A & M University System: College Station, TX, 1987
    • TRC Thermodynamic Tables - Hydrocarbons; Thermodynamic Research Center, The Texas A & M University System: College Station, TX, 1987.
  • 83
    • 0003391553 scopus 로고
    • CRC Press, Boca Raton, 1983; 2nd revised ed
    • N. Trinajstić, Chemical Graph Theory, CRC Press, Boca Raton, 1983; 2nd revised ed. 1992.
    • (1992) Chemical Graph Theory
    • Trinajstić, N.1
  • 86
    • 63149187098 scopus 로고    scopus 로고
    • Note on the graphs with the greatest edge-Szeged index
    • D. Vukičević, Note on the graphs with the greatest edge-Szeged index, MATCH Commun. Math. Comput. Chem. 61 (2009) 673-681.
    • (2009) MATCH Commun. Math. Comput. Chem. , vol.61 , pp. 673-681
    • Vukičević, D.1
  • 87
    • 70350166990 scopus 로고    scopus 로고
    • Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges
    • D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369-1376.
    • (2009) J. Math. Chem. , vol.46 , pp. 1369-1376
    • Vukičević, D.1    Furtula, B.2
  • 89
    • 0001020629 scopus 로고    scopus 로고
    • The phenylenes: Synthesis, properties, and reactivity
    • B. Halton (Ed.), JAI Press, London
    • K. P. C. Vollhardt, D. L. Mohler, The phenylenes: Synthesis, properties, and reactivity, in: B. Halton (Ed.), Advances in Strain in Organic Chemistry, Vol. 5, JAI Press, London, 1996, pp. 121-160.
    • (1996) Advances in Strain in Organic Chemistry , vol.5 , pp. 121-160
    • Vollhardt, K.P.C.1    Mohler, D.L.2
  • 90
    • 8544254107 scopus 로고
    • Structural determination of paraffin boiling points
    • H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17-20.
    • (1947) J. Am. Chem. Soc. , vol.69 , pp. 17-20
    • Wiener, H.1
  • 91
    • 80051490242 scopus 로고    scopus 로고
    • The geometric-arithmetic index of benzenoid systems and phenylenes
    • L. Xiao, S. Chen, Z. Guo, Q. Chen, The geometric-arithmetic index of benzenoid systems and phenylenes, Int. J. Contemp. Math. Sci. 5 (2010) 2225-2230.
    • (2010) Int. J. Contemp. Math. Sci. , vol.5 , pp. 2225-2230
    • Xiao, L.1    Chen, S.2    Guo, Z.3    Chen, Q.4
  • 93
    • 79952460398 scopus 로고    scopus 로고
    • Maximum Wiener index of trees with given degree sequence
    • X. D. Zhang, Y. Liu, M. X. Han, Maximum Wiener index of trees with given degree sequence, MATCH Commun. Math. Comput. Chem. 64 (2010) 661-682.
    • (2010) MATCH Commun. Math. Comput. Chem. , vol.64 , pp. 661-682
    • Zhang, X.D.1    Liu, Y.2    Han, M.X.3
  • 94
  • 96
    • 72149130565 scopus 로고    scopus 로고
    • On two types of geometric-arithmetic index
    • B. Zhou, I. Gutman, B. Furtula, Z. Du, On two types of geometric-arithmetic index, Chem. Phys. Lett. 482 (2009) 153-155.
    • (2009) Chem. Phys. Lett. , vol.482 , pp. 153-155
    • Zhou, B.1    Gutman, I.2    Furtula, B.3    Du, Z.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.