Some results on the distance and distance signless Laplacian spectral radius of graphs and digraphs

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• 作者：Dan Li^a ; Guoping Wang^b ; Jixiang Meng ; ^a ; ^{ldxjedu@163.com" class="auth_mail" title="E-mail the corresponding author} ; ^{mjxxju@sina.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Distance matrix ; Distance signless Laplacian matrix ; Dichromatic number ; Spectral radius
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：293
• 期：Complete
• 页码：218-225
• 全文大小：364 K

文摘

Let ρ(D(G)) denote the distance spectral radius of a graph G   and $\partial \left(\overrightarrow{G}\right)$ denote the distance signless Laplacian spectral radius of a digraph $\overrightarrow{G}$. Let ${\mathcal{G}}_{n,k}^D$ be the set of all k-connected graphs of order n with diameter D  . In this paper, we first determine the unique graph with minimum distance spectral radius in ${\mathcal{G}}_{n,k}^D$; we then give sharp upper and lower bounds for the distance signless Laplacian spectral radius of strongly connected digraphs; we also characterize the digraphs having the maximal and minimal distance signless Laplacian spectral radii among all strongly connected digraphs; furthermore, we determine the extremal digraph with the minimal distance signless Laplacian spectral radius with given dichromatic number.