# A characterization of strongly regular graphs in terms of the largest signless Laplacian eigenvalues

Feng Lei Fan*, Chih-wen Weng

*此作品的通信作者

1 引文 斯高帕斯（Scopus）

## 摘要

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) 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).

原文 English 1-5 5 Linear Algebra and Its Applications 506 https://doi.org/10.1016/j.laa.2016.05.009 Published - 1 10月 2016