منابع مشابه
Bounds on graph eigenvalues I
We improve some recent results on graph eigenvalues. In particular, we prove that if G is a graph of order n 2; maximum degree ; and girth at least 5; then
متن کاملBounds on graph eigenvalues II
We prove three results about the spectral radius μ (G) of a graph G : (a) Let Tr (n) be the r-partite Turán graph of order n. If G is a Kr+1-free graph of order n, then μ (G) < μ (Tr (n)) unless G = Tr (n) . (b) For most irregular graphs G of order n and size m, μ (G)− 2m/n > 1/ (2m+ 2n) . (c) Let 0 ≤ k ≤ l. If G is a graph of order n with no K2 +Kk+1 and no K2,l+1, then μ (G) ≤ min {
متن کاملBounds for Laplacian Graph Eigenvalues
Let G be a connected simple graph whose Laplacian eigenvalues are 0 = μn (G) μn−1 (G) · · · μ1 (G) . In this paper, we establish some upper and lower bounds for the algebraic connectivity and the largest Laplacian eigenvalue of G . Mathematics subject classification (2010): 05C50, 15A18.
متن کاملBounds for Eigenvalues of a Graph
New lower bounds for eigenvalues of a simple graph are derived. Upper and lower bounds for eigenvalues of bipartite graphs are presented in terms of traces and degree of vertices. Finally a non-trivial lower bound for the algebraic connectivity of a connected graph is given.
متن کاملA ug 2 00 6 Bounds on graph eigenvalues
We improve some recent results on graph eigenvalues. In particular, we prove that if G is a graph of order n ≥ 2, maximum degree ∆, and girth at least 5, then μ (G) ≤ min {
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.08.020