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Volumn 373, Issue SUPPL., 2003, Pages 241-272

Which graphs are determined by their spectrum?

Author keywords

Cospectral graphs; Distance regular graphs; Eigenvalues; Spectra of graphs

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; LAPLACE TRANSFORMS;

EID: 0141607701     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(03)00483-X     Document Type: Conference Paper
Times cited : (652)

References (68)
  • 1
    • 0038893539 scopus 로고
    • A strongly regular graph derived from the perfect ternary Golay code
    • J.N. Shrivastava. Amsterdam: North-Holland
    • Berlekamp E.R., van Lint J.H., Seidel J.J. A strongly regular graph derived from the perfect ternary Golay code. Shrivastava J.N. A Survey in Combinatorial Theory. 1973;25-30 North-Holland, Amsterdam.
    • (1973) A Survey in Combinatorial Theory , pp. 25-30
    • Berlekamp, E.R.1    Van Lint, J.H.2    Seidel, J.J.3
  • 3
    • 84972549301 scopus 로고
    • Strongly regular graphs, partial geometries and partially balanced designs
    • Bose R.C. Strongly regular graphs, partial geometries and partially balanced designs. Pacific J. Math. 13:1963;389-419.
    • (1963) Pacific J. Math. , vol.13 , pp. 389-419
    • Bose, R.C.1
  • 4
    • 84987492195 scopus 로고
    • Almost all trees share a complete set of immanantal polynomials
    • Botti P., Merris R. Almost all trees share a complete set of immanantal polynomials. J. Graph Theory. 17:1993;467-476.
    • (1993) J. Graph Theory , vol.17 , pp. 467-476
    • Botti, P.1    Merris, R.2
  • 6
    • 84986518967 scopus 로고
    • The uniqueness of the strongly regular graph on 77 points
    • Brouwer A.E. The uniqueness of the strongly regular graph on 77 points. J. Graph Theory. 7:1983;455-461.
    • (1983) J. Graph Theory , vol.7 , pp. 455-461
    • Brouwer, A.E.1
  • 7
    • 0009030635 scopus 로고    scopus 로고
    • Strongly regular graphs
    • C.J. Colbourn, & J.H. Denitz. CRC Press
    • Brouwer A.E. Strongly regular graphs. Colbourn C.J., Denitz J.H. The CRC Handbook of Combinatorial Designs. 1996;667-685 CRC Press.
    • (1996) The CRC Handbook of Combinatorial Designs , pp. 667-685
    • Brouwer, A.E.1
  • 9
    • 0038410906 scopus 로고
    • The Gewirtz graph: An exercise in the theory of graph spectra
    • Brouwer A.E., Haemers W.H. The Gewirtz graph: An exercise in the theory of graph spectra. European J. Combin. 14:1993;397-407.
    • (1993) European J. Combin. , vol.14 , pp. 397-407
    • Brouwer, A.E.1    Haemers, W.H.2
  • 10
    • 38249010273 scopus 로고
    • Structure and uniqueness of the ( 81,20,1,6 ) strongly regular graph
    • Brouwer A.E., Haemers W.H. Structure and uniqueness of the (. 81,20,1,6 ) strongly regular graph Discrete Math. 106/107:1992;77-82.
    • (1992) Discrete Math. , vol.106-107 , pp. 77-82
    • Brouwer, A.E.1    Haemers, W.H.2
  • 12
    • 0011295841 scopus 로고
    • Graphs related to exceptional root systems
    • Eindhoven University of Technology
    • F.C. Bussemaker, D.M. Cvetković, J.J. Seidel, Graphs related to exceptional root systems, T.H.-Report 76-WSK-05, Eindhoven University of Technology, 1976.
    • (1976) T.H.-Report , vol.76 WSK-05
    • Bussemaker, F.C.1    Cvetković, D.M.2    Seidel, J.J.3
  • 13
    • 0001438198 scopus 로고
    • Strongly regular graph having strongly regular subconstituents
    • Cameron P.J., Goethals J.M., Seidel J.J. Strongly regular graph having strongly regular subconstituents. J. Algebra. 55:1978;257-280.
    • (1978) J. Algebra , vol.55 , pp. 257-280
    • Cameron, P.J.1    Goethals, J.M.2    Seidel, J.J.3
  • 18
  • 20
    • 0042644229 scopus 로고
    • Constructing trees with given eigenvalues and angles
    • Cvetković D.M. Constructing trees with given eigenvalues and angles. Linear Algebra Appl. 105:1988;1-8.
    • (1988) Linear Algebra Appl. , vol.105 , pp. 1-8
    • Cvetković, D.M.1
  • 21
    • 0141707483 scopus 로고
    • Root systems, forbidded subgraphs and spectral characterizations of line graphs
    • Cvetković, Gutman, Pisanski, Tošić (Eds.) Novi Sad
    • D.M. Cvetković, M. Doob, Root systems, forbidded subgraphs and spectral characterizations of line graphs, in: Cvetković, Gutman, Pisanski, Tošić (Eds.) Graph Theory, Proc. Fourth Yugoslav Sem. Graph Theory, Novi Sad, 1983, pp. 69-99.
    • (1983) Graph Theory, Proc. Fourth Yugoslav Sem. Graph Theory , pp. 69-99
    • Cvetković, D.M.1    Doob, M.2
  • 23
    • 0004092833 scopus 로고
    • first edition: Deutscher Verlag der Wissenschaften, Berlin, 1980; Academic Press, New York, 1980. Johann Abrosius Barth Verlag
    • Cvetković D.M., Doob M., Sachs H. Spectra of Graphs. first edition: Deutscher Verlag der Wissenschaften, Berlin, 1980; Academic Press, New York, 1980 third ed. 1995;Johann Abrosius Barth Verlag.
    • (1995) Spectra of Graphs. Third ED.
    • Cvetković, D.M.1    Doob, M.2    Sachs, H.3
  • 25
    • 22044434252 scopus 로고
    • Regular graphs with four eigenvalues
    • van Dam E.R. Regular graphs with four eigenvalues. Linear Algebra Appl. 226-228:1995;139-162.
    • (1995) Linear Algebra Appl. , vol.226-228 , pp. 139-162
    • Van Dam, E.R.1
  • 26
    • 0011367968 scopus 로고    scopus 로고
    • Nonregular graphs with three eigenvalues
    • van Dam E.R. Nonregular graphs with three eigenvalues. J. Combin. Theory B. 73:1998;101-118.
    • (1998) J. Combin. Theory B , vol.73 , pp. 101-118
    • Van Dam, E.R.1
  • 27
    • 0038829967 scopus 로고    scopus 로고
    • Graphs with constant μ and μ̄
    • van Dam E.R., Haemers W.H. Graphs with constant. μ and μ Discrete Math. 182:1998;293-307.
    • (1998) Discrete Math. , vol.182 , pp. 293-307
    • Van Dam, E.R.1    Haemers, W.H.2
  • 28
    • 31244432796 scopus 로고    scopus 로고
    • Spectral characterizations of some distance-regular graphs
    • van Dam E.R., Haemers W.H. Spectral characterizations of some distance-regular graphs. J. Algebra Combin. 15:2002;189-202.
    • (2002) J. Algebra Combin. , vol.15 , pp. 189-202
    • Van Dam, E.R.1    Haemers, W.H.2
  • 30
    • 0041783284 scopus 로고    scopus 로고
    • Small regular graphs with four eigenvalues
    • van Dam E.R., Spence E. Small regular graphs with four eigenvalues. Discrete Math. 189:1998;233-257.
    • (1998) Discrete Math. , vol.189 , pp. 233-257
    • Van Dam, E.R.1    Spence, E.2
  • 32
    • 0141707484 scopus 로고
    • Seidel switching and cospectral graphs with four distinct eigenvalues
    • Doob D.M. Seidel switching and cospectral graphs with four distinct eigenvalues. Ann. New York Acad. Sci. 319:1979;164-168.
    • (1979) Ann. New York Acad. Sci. , vol.319 , pp. 164-168
    • Doob, D.M.1
  • 33
    • 31244435712 scopus 로고    scopus 로고
    • The complement of the path is determined by its spectrum
    • Doob M., Haemers W.H. The complement of the path is determined by its spectrum. Linear Algebra Appl. 356:2002;57-65.
    • (2002) Linear Algebra Appl. , vol.356 , pp. 57-65
    • Doob, M.1    Haemers, W.H.2
  • 34
    • 0031281101 scopus 로고    scopus 로고
    • From local adjacency polynomials to locally pseudo-distance-regular graphs
    • Fiol M.A., Garriga E. From local adjacency polynomials to locally pseudo-distance-regular graphs. J. Combin. Theory B. 71:1997;162-183.
    • (1997) J. Combin. Theory B , vol.71 , pp. 162-183
    • Fiol, M.A.1    Garriga, E.2
  • 35
    • 29444443527 scopus 로고
    • On hearing the shape of a drum
    • Fisher M. On hearing the shape of a drum. J. Combin. Theory. 1:1966;105-125.
    • (1966) J. Combin. Theory , vol.1 , pp. 105-125
    • Fisher, M.1
  • 36
    • 0141818750 scopus 로고    scopus 로고
    • Isospectral graphs and isoperimetric constants
    • Fujii H., Katsuda A. Isospectral graphs and isoperimetric constants. Discrete Math. 207:1999;33-52.
    • (1999) Discrete Math. , vol.207 , pp. 33-52
    • Fujii, H.1    Katsuda, A.2
  • 37
    • 0141484143 scopus 로고
    • Graphs with maximal even girth
    • Gewitz A. Graphs with maximal even girth. Canad. J. Math. 21:1969;915-934.
    • (1969) Canad. J. Math. , vol.21 , pp. 915-934
    • Gewitz, A.1
  • 39
    • 0141818748 scopus 로고
    • Some computational results on the spectra of graphs
    • Combinatorial Mathematics IV (Proceedings of the Fourth Australian Conference on Combinatorial Mathematics, Adelaide) L.R.A. Casse, & W.D. Wallis. Berlin: Springer-Verlag
    • Godsil C.D., McKay B.D. Some computational results on the spectra of graphs. Casse L.R.A., Wallis W.D. Combinatorial Mathematics IV (Proceedings of the Fourth Australian Conference on Combinatorial Mathematics, Adelaide). Lecture Notes in Mathematics. vol. 560:1976;73-92 Springer-Verlag, Berlin.
    • (1976) Lecture Notes in Mathematics , vol.560 , pp. 73-92
    • Godsil, C.D.1    McKay, B.D.2
  • 40
  • 41
    • 0000293849 scopus 로고
    • The regular two-graph on 276 vertices
    • Goethals J.M., Seidel J.J. The regular two-graph on 276 vertices. Discrete Math. 12:1975;143-158.
    • (1975) Discrete Math. , vol.12 , pp. 143-158
    • Goethals, J.M.1    Seidel, J.J.2
  • 42
    • 0039371782 scopus 로고
    • Zusammenhang von Graphentheorie und MO-Theorie von Molekeln mit Systemen konjugierter Bindungen
    • Günthard Hs.H., Primas H. Zusammenhang von Graphentheorie und MO-Theorie von Molekeln mit Systemen konjugierter Bindungen. Helv. Chim. Acta. 39:1956;1645-1653.
    • (1956) Helv. Chim. Acta , vol.39 , pp. 1645-1653
    • Günthard, Hs.H.1    Primas, H.2
  • 43
    • 0030535554 scopus 로고    scopus 로고
    • Distance-regularity and the spectrum of graphs
    • Haemers W.H. Distance-regularity and the spectrum of graphs. Linear Algebra Appl. 236:1996;265-278.
    • (1996) Linear Algebra Appl. , vol.236 , pp. 265-278
    • Haemers, W.H.1
  • 45
    • 0141484145 scopus 로고    scopus 로고
    • Enumeration of cospectral graphs
    • in press
    • W.H. Haemers, E. Spence, Enumeration of cospectral graphs, European J. Combin., in press. Also: Center discussion paper 2002-90, Tilburg University.
    • European J. Combin.
    • Haemers, W.H.1    Spence, E.2
  • 46
    • 0141818752 scopus 로고    scopus 로고
    • Tilburg University
    • W.H. Haemers, E. Spence, Enumeration of cospectral graphs, European J. Combin., in press. Also: Center discussion paper 2002-90, Tilburg University.
    • Center Discussion Paper , vol.2002 , Issue.90
  • 48
    • 0347318522 scopus 로고    scopus 로고
    • Reconstruction of weighted graphs by their spectrum
    • Halbeisen L., Hungerbühler N. Reconstruction of weighted graphs by their spectrum. European J. Combin. 21:2000;641-650.
    • (2000) European J. Combin. , vol.21 , pp. 641-650
    • Halbeisen, L.1    Hungerbühler, N.2
  • 49
    • 0002935888 scopus 로고
    • On the polynomial of a graph
    • Hoffman A.J. On the polynomial of a graph. Amer. Math. Monthly. 70:1963;30-36.
    • (1963) Amer. Math. Monthly , vol.70 , pp. 30-36
    • Hoffman, A.J.1
  • 50
    • 0141484144 scopus 로고    scopus 로고
    • Spectral characterization of some generalized odd graphs
    • Huang T., Liu C. Spectral characterization of some generalized odd graphs. Graphs Combin. 15:1999;195-209.
    • (1999) Graphs Combin. , vol.15 , pp. 195-209
    • Huang, T.1    Liu, C.2
  • 52
    • 0002697827 scopus 로고
    • Can one hear the shape of a drum?
    • Kac M. Can one hear the shape of a drum? Amer. Math. Monthly. 73:1966;1-23.
    • (1966) Amer. Math. Monthly , vol.73 , pp. 1-23
    • Kac, M.1
  • 53
    • 31244437055 scopus 로고    scopus 로고
    • No starlike trees are cospectral
    • Lepović M., Gutman I. No starlike trees are cospectral. Discrete Math. 242:2002;291-295.
    • (2002) Discrete Math. , vol.242 , pp. 291-295
    • Lepović, M.1    Gutman, I.2
  • 55
    • 0002093056 scopus 로고
    • Cayley graphs: Eigenvalues, expanders and random walks
    • Surveys in Combinatorics, 1995 (Stirling) Cambridge: Cambridge University Press
    • Lubotzky A. Cayley graphs: eigenvalues, expanders and random walks. in: Surveys in Combinatorics, 1995 (Stirling). London Math. Soc. Lecture Note Ser. vol. 218:1995;155-189 Cambridge University Press, Cambridge.
    • (1995) London Math. Soc. Lecture Note Ser. , vol.218 , pp. 155-189
    • Lubotzky, A.1
  • 56
    • 0001633258 scopus 로고
    • On the spectral characterisation of trees
    • McKay B.D. On the spectral characterisation of trees. Ars Combin. 3:1979;219-232.
    • (1979) Ars Combin. , vol.3 , pp. 219-232
    • McKay, B.D.1
  • 57
    • 0141818749 scopus 로고    scopus 로고
    • Classification of regular two-graphs on 36 and 38 vertices
    • McKay B.D., Spence E. Classification of regular two-graphs on 36 and 38 vertices. Austral. J. Combin. 24:2001;293-300.
    • (2001) Austral. J. Combin. , vol.24 , pp. 293-300
    • McKay, B.D.1    Spence, E.2
  • 58
    • 21944445400 scopus 로고    scopus 로고
    • Large families of Laplacian isospectral graphs
    • Merris R. Large families of Laplacian isospectral graphs. Linear and Multilinear Algebra. 43:1997;201-205.
    • (1997) Linear and Multilinear Algebra , vol.43 , pp. 201-205
    • Merris, R.1
  • 60
    • 0141595687 scopus 로고    scopus 로고
    • The characteristic polynomials of modified graphs
    • Rowlinson P. The characteristic polynomials of modified graphs. Discrete Appl. Math. 67:1996;209-219.
    • (1996) Discrete Appl. Math. , vol.67 , pp. 209-219
    • Rowlinson, P.1
  • 61
    • 0040513949 scopus 로고
    • Über Teiler, Faktoren und charakteristische Polynome von Graphen, Teil II
    • H. Sachs, Über Teiler, Faktoren und charakteristische Polynome von Graphen, Teil II, Wiss. Z. TH Ilmenau 13 (1967) 405-412.
    • (1967) Wiss. Z. TH Ilmenau , vol.13 , pp. 405-412
    • Sachs, H.1
  • 62
    • 0002874852 scopus 로고
    • Almost all trees are cospectral
    • F. Harary. New York: Academic Press
    • Schwenk A.J. Almost all trees are cospectral. Harary F. New Directions in the Theory of Graphs. 1973;275-307 Academic Press, New York.
    • (1973) New Directions in the Theory of Graphs , pp. 275-307
    • Schwenk, A.J.1
  • 63
    • 0010134107 scopus 로고
    • Strongly regular graphs with ( -1,1,0 ) adjacency matrix having eigenvalue 3
    • Seidel J.J. Strongly regular graphs with (. -1,1,0 ) adjacency matrix having eigenvalue 3 Linear Algebra Appl. 1:1968;198-281.
    • (1968) Linear Algebra Appl. , vol.1 , pp. 198-281
    • Seidel, J.J.1
  • 64
    • 0141595688 scopus 로고
    • Graphs and two-graphs
    • F. Hoffman et al. (Eds.), Utilitas Mathematica Pub., Winnipeg
    • J.J. Seidel, Graphs and two-graphs, in: F. Hoffman et al. (Eds.) Proc. 5th Southeast. Conf. Comb., Graph Th., Comp., Utilitas Mathematica Pub., Winnipeg, 1974, pp. 125-143.
    • (1974) Proc. 5th Southeast. Conf. Comb., Graph Th., Comp. , pp. 125-143
    • Seidel, J.J.1
  • 65
    • 0001694338 scopus 로고
    • A survey of two-graphs
    • Teorie Combinatorie, Roma 1973, Accad. Nac. Lincei, Roma
    • J.J. Seidel, A survey of two-graphs, in: Teorie Combinatorie (Proc. Intern. Coll., Roma 1973), Accad. Nac. Lincei, Roma, 1976, pp. 481-511.
    • (1976) Proc. Intern. Coll. , pp. 481-511
    • Seidel, J.J.1
  • 66
    • 0141779208 scopus 로고    scopus 로고
    • Large families of cospectral graphs
    • Seress Á. Large families of cospectral graphs. Designs, Codes and Cryptography. 21:2000;205-208.
    • (2000) Designs, Codes and Cryptography , vol.21 , pp. 205-208
    • Seress, Á.1
  • 68
    • 0001270387 scopus 로고
    • Congruent graphs and the connectivity of graphs
    • Whitney H. Congruent graphs and the connectivity of graphs. Amer. J. Math. 54:1932;150-167.
    • (1932) Amer. J. Math. , vol.54 , pp. 150-167
    • Whitney, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.