Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4600811 | Linear Algebra and its Applications | 2011 | 5 Pages |
Abstract
Let G = (V, E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G) = D(G) + A(G ). In [5], Cvetković et al. have given the following conjecture involving the second largest signless Laplacian eigenvalue (q2q2) and the index (λ1λ1) of graph G (see also Aouchiche and Hansen [1]):1-n-1⩽q2-λ1⩽n-2-2n-4with equality if and only if G is the star K1,n-1K1,n-1 for the lower bound, and if and only if G is the complete bipartite graph Kn-2,2Kn-2,2 for the upper bound. In this paper we prove the lower bound and characterize the extremal graphs.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kinkar Ch. Das,