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COMBINATORICS
2007
100views more  COMBINATORICS 2007»
15 years 6 months ago
Revisiting Two Classical Results on Graph Spectra
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) If H is a proper subgraph of a connected graph G o...
Vladimir Nikiforov
COMBINATORICA
2000
105views more  COMBINATORICA 2000»
15 years 6 months ago
On Cayley Graphs on the Symmetric Group Generated by Tranpositions
Given a connected graph, X, we denote by 2 = 2(X) its smallest non-zero Laplacian eigenvalue. In this paper we show that among all sets of n - 1 transpositions which generate the ...
Joel Friedman
COMBINATORICS
2002
83views more  COMBINATORICS 2002»
15 years 6 months ago
Identifying Codes with Small Radius in Some Infinite Regular Graphs
Let G = (V, E) be a connected undirected graph and S a subset of vertices. If for all vertices v V , the sets Br(v) S are all nonempty and different, where Br(v) denotes the set...
Irène Charon, Olivier Hudry, Antoine Lobste...
EJC
2006
15 years 6 months ago
Invariant subspaces, duality, and covers of the Petersen graph
A general method for finding elementary abelian regular covering projections of finite connected graphs is applied to the Petersen graph. As a result, a complete list of pairwise ...
Aleksander Malnic, Primoz Potocnik
DM
2000
115views more  DM 2000»
15 years 6 months ago
Dualizability and graph algebras
We characterize the finite graph algebras which are dualizable. Indeed, a finite graph algebra is dualizable if and only if each connected component of the underlying graph is eith...
Brian A. Davey, Pawel M. Idziak, William A. Lampe,...