On the eigenvalues of a graphAllen SchwenkRobin J Wilson
On the eigenvalues of A α -matrix of graphs 来自 Semantic Scholar 喜欢 0 阅读量: 141 作者:S Liu,KC Das,J Shu 摘要: Let G be a graph with adjacency matrix A(G) and let D(G) be the diagonal matrix of the degrees of G. For every real α∈[0,1], Nikiforov defined the matrix...
The eigenvalues of multiplicity one are called the simple eigenvalues. The equation Ax=λx is called the eigenvalue equation of A, or of a labeled graph G if A=A(G). For a fixed λ∈Sp(G), its non-trivial solution x=(x1,x2,…,xn)T is a λ-eigenvector of A, or of a ...
Under an Elsevieruser license open archive Abstract Letλ1(G)⩾⋯⩾λn(G)be the eigenvalues of a graphG. We explore the distribution of eigenvalues of a graphGwithλ3(G)<0and prove that−1⩽λk(G)<0for3⩽k⩽n+12,λk(G)⩽−1forn+32⩽k⩽n(n⩾5)andλn(G)...
afzal@yahoo.comAbstractA design graph is a regular bipartite graph in which any two distinctvertices of the same part have the same number of common neighbors.This class of graphs have a close relationship to strongly regular graphs.In this paper, we study the distance eigenvalues of the ...
On the Laplacian Eigenvalues of Signed Graphs 来自 Taylor & Francis 喜欢 0 阅读量: 253 作者:Y Hou,J Li,Y Pan 摘要: A signed graph is a graph with a sign attached to each edge. This article extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In ...
On the Laplacian eigenvalues of a graph In the note, we present an upper bound for the spectral radius of Laplacian matrix of a graph in terms of a “2-degree” of a vertex. LXD Zhang - 《Linear Algebra & Its Applications》 被引量: 441发表: 1998年 A note on the signless Laplacian...
eigenvaluesgraphsdistributionlemmaverticesgraph On the distribution of eigenvalues of graphs Xuerong Yong Department of Mathematics, Xinjiang University, Urumqi 830046, P.R.China Abstract Let G be a simple graph with n(≥ 2) vertices, and λ i (G) be the ith largest eigenvalue of G. In this...
More spectral bounds on the clique and independence numbers We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues. In particular we prove the following results. Let G... V Nikiforov - Academic Press, Inc. 被引量: 41发表: 2009年 On a Pos...
On the extreme eigenvalues of regular graphs - Cioabǎ - 2005 () Citation Context ...3 nm (n 2 − 2m) with equality if and only if G is a regular complete multipartite graph. (5) From Theorem 3 we effortlessly deduce results complementary to results of Serre, Li, and Cioabă (...