A lower bound on the spectral radius of the universal cover of a graph

Journal of Combinatorial Theory. Series B

Volumn 93, Issue 1, 2005, Pages 33-43

  Hoory, Shlomo ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Average degree; Eigenvalues; Graph; Spectral radius; Universal cover

Indexed keywords

EID: 8844259732     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jctb.2004.06.001     Document Type: Article

References (11)

1. Alon N. Hoory S. Linial N. The Moore bound for irregular graphs Graphs Combin. 18 1 2002 53-57
2. Friedman J. Some geometric aspects of graphs and their eigenfunctions Duke Math. J. 69 3 1993 487-525
3. Godsil C.D. Mohar B. Walk generating functions and spectral measures of infinite graphs Linear Algebra Appl. 107 1988 191-206
4. Y. Greenberg, Ph.D. Thesis, Hebrew University of Jerusalem, 1995 (in Hebrew).
5. Hoory S. The size of bipartite graphs with a given girth J. Combin. Theory Ser. B 86 2 2002 215-220
6. A. Lubotzky, Discrete Groups, Expanding Graphs and Invariant Measures, Progress in Mathematics, Vol. 125, Birkhäuser Verlag, Basel, 1994 (With an appendix by Jonathan D. Rogawski).
7. Lubotzky A. Phillips R. Sarnak P. Ramanujan graphs Combinatorica 8 3 1988 261-277
8. Margulis G.A. Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators Problemy Peredachi Informatsii 24 1 1988 51-60
9. Morgenstern M. Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q J. Combin. Theory Ser. B 62 1 1994 44-62
10. T. Nagnibeda, Random walks on trees, spectral radii of groups, and Ramanujan graphs, Manuscript, 2003.
11. Nilli A. On the second eigenvalue of a graph Discrete Math. 91 2 1991 207-210