Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598467 | Linear Algebra and its Applications | 2016 | 5 Pages |
Abstract
Let G be a simple graph of order n with maximum degree Δ. Let λ (resp. μ) denote the maximum number of common neighbors of a pair of adjacent vertices (resp. nonadjacent distinct vertices) of G . Let q(G)q(G) denote the largest eigenvalue of the signless Laplacian matrix of G. We show thatq(G)≤Δ−μ4+(Δ−μ4)2+(1+λ)Δ+μ(n−1)−Δ2, with equality if and only if G is a strongly regular graph with parameters (n,Δ,λ,μ)(n,Δ,λ,μ).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Feng-lei Fan, Chih-wen Weng,