双圈图补图的距离无符号拉普拉斯谱半径

Distance Signless Laplacian Spectral Radius of the Complements of Bicyclic Graphs

摘要: 设G是简单连通图，$D^Q\left(G\right)=Tr\left(G\right)+D\left(G\right)$ 为图G的距离无符号拉普拉斯矩阵，其中$Tr\left(G\right)$ 和$D\left(G\right)$ 分别是图G的点传递对角矩阵和距离矩阵。本文在n阶双圈图补图中确定了距离无符号拉普拉斯谱半径最大时所落在的图类集合。

Abstract: Let G be a simple connected graph, and $D^Q\left(G\right)=Tr\left(G\right)+D\left(G\right)$ be the distance signless Laplacian matrix of graph G, where $Tr\left(G\right)$ and $D\left(G\right)$ are diagonal matrix with vertex transmissions of G and distance matrix of G, respectively. This article determines the set of graph classes that fall at the maximum distance from signless Laplacian spectral radius in the complements of bicyclic graphs with n-order.