Laplacian spectra and spanning trees of threshold graphs

Discrete Applied Mathematics

Volumn 65, Issue 1-3, 1996, Pages 255-273

  Hammer, P L ^a   Kelmans, A K ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005232065     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0166-218X(94)00049-J     Document Type: Article

References (38)

1. C. Berge, Theory of Graphs and its Applications (Methuen, London 1962).
2. J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (MacMillan, New York, 1976).
3. R.C. Bose, Strongly regular graphs, partial geometries and partially balanced designs. Pacific J. Math. 13 (1963) 389-419.
4. A. Brandstädt, Special graph classes - a survey, Section Math, Fredrich Schiller Universität, Jena (1991).
5. R.A. Brualdi and H.J. Ryser, Combinatorial Matrix Theory (Cambridge University Press, Cambridge, 1991).
6. V. Chvátal and P.L. Hammer, Aggregation of inequalities in integer programming, Ann. Discrete Math. 1 (1977) 145-162.
7. G.M. Constantine, Combinatorial Theory and Statistical Delabel (Wiley, New York, 1987).
8. D. Cvetković, Graphs and their spectra, Elektrohn. Fak. Ser. Mat. Fiz. 354-356 (1971) 1-50.
9. D. Cvetković and M. Doob, Developments in the theory of graph spectra, Linear and Multilinear Algebra 18 (1985) 153-181.
10. D. Cvetković, M. Doob and H. Sachs, Spectra of Graphs. Theory and Applications (Academic Press, New York, 1980).
11. C. Delorme and S. Poljak, Laplacian eigenvalues and the maximum cut problem, in press.
12. E.A. Dinic, A.K. Kelmans and M.A. Zaitcev, Non-isomorphic trees with the same T-polynomials, Inform. Process. Lett. 6 (1977) 73-76.
13. M. Doob, On characterizing certain graphs with four eigenvalues by their spectra, Linear Algebra Appl. 3 (1970) 461-482.
14. M. Doob, A spectral characterization of the line graph of a BIBD with γ = 1, Linear Algebra Appl. 12 (1975) 11-20.
15. P. Erdos and T. Gallai, Graphen mit Punkten vorgeschreibenen Grades, Mat. Lapok 11 (1960) 264-274.
16. M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973) 298-305.
17. M. Ch. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, New York, 1980).
18. R. Grone, R. Merris and V.S. Sunders, The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl. 11 (1990) 218-235.
19. P.L. Hammer, T. Ibaraki and B. Simeone, Threshold sequences, SIAM J. Algebraic Discrete Methods 2 (1981) 39-49.
20. F. Harary, Graph Theory (Addison-Wesley, Reading, MA, 1969).
21. A.J. Hoffman, On the line graph of a projective plane, Proc. Amer. Math. Soc. 16 (1965) 297-302.
22. A.J. Hoffman and D.K. Ray-Chaudhuri, On the line graph of a finite affine plane, Canad. J. Math. 17 (1965) 687-694.
23. A.J. Hoffman and D.K. Ray-Chaudhuri, On the line graph of a symmetric balanced incomplete block design, Trans. Amer. Math. Soc. 116 (1965) 238-252.
24. A.K. Kelmans, The capability of distinguishing of the characteristic polynomial of the conductive matrix of a graph (1964) (unpublished, described in [8, 10]).
25. A.K. Kelmans, The number of trees of a graph I, II, Avtomat. i Telemekh. (Automat. Remote Control) 26 (1965) 2194-2204, 27 (1966) 56-65 (in Russian).
26. A.K. Kelmans, The number of trees of a graph I, II, Avtomat. i Telemekh. (Automat. Remote Control) 26 (1965) 2194-2204, 27 (1966) 56-65 (in Russian).
27. A.K. Kelmans, On properties of the characteristic polynomial of a graph, in: Kibern. na Sl. Kom. 4 (Energiya, Moscow, 1967) (in Russian).
28. A.K. Kelmans, On the determination of the eigenvalues of some special matrices, Ekonom. Mat. Metody 8 (1972) 266-272 (in Russian).
29. A.K. Kelmans, Comparison of graphs by their number of spanning trees, Discrete Math. 16 (1976) 241-261.
30. A.K. Kelmans, On graphs with the extremal numbers of spanning trees, J. Graph Theory 4 (1980) 119-122.
31. A.K. Kelmans and V.M. Chelnokov, A certain polynomial of a graph and graphs with an extremal number of trees, J. Combin. Theory Ser. B 16 (1974) 197-214.
32. S.-Y.R. Li, Graphic sequences with unique realization, J. Combin. Theory Ser. B 19 (1975) 42-68.
33. N.V.R. Mahadev and U.N. Peled,Threshold graphs (monograph), Ann. Discrete Math, forthcoming.
34. J.W. Moon, Enumerating labeled trees, in: F. Harary, ed., Graph Theory and Theoretical Physics (Academic Press, New York, 1967) 261-272.
35. A. Mowshowitz, The characteristic polynomial of a graph, J. Combin. Theory Ser B 12 (1972) 177-193.
36. 2 association scheme, Ann. Math. Statist. 30 (1959) 781-798.
37. A.J. Shwenk, Almost all trees are cospectral, in: F. Harary, ed., New Directions in the Theory of Graphs (Academic Press, New York, 1973) 257-307.
38. W.T. Tutte, All the king's horses, in: J.A. Bondy and U.S.R. Murty, eds., Graph Theory and Related Topics (Academic Press, New York, 1979).