双圈图的补图的无符号拉普拉斯谱半径

The Signless Laplacian Spectral Radius of the Complement of Bicyclic Graphs

设D(G)和A(G)分别是图G的度矩阵和邻接矩阵,则Q(G)=D(G)+A(G)就是G的无符号拉普拉斯矩阵。让Un3是把n−3条悬挂边粘到3圈C3上的一点后得到的单圈图,θn∗是把n−4条悬挂边粘到θ (2,1,2)的一个三度点得到的双圈图。在这篇文章里我们证明了,取得最大无符号拉普拉斯谱半径的单圈图和双圈图分别是Un3和θn∗。

Let D(G) and A(G) be degree matrix and adjacency matrix of graph G, respectively. Then the signless Laplacian matrix is defined as Q(G)=D(G)+A(G). Let Un3 be the unicyclic graph ob-tained by attaching n−3 pendent edges to a vertex on C3, and θn∗ be the bicyclic graph ob-tained by attaching n−4 pendent edges to a vertex of degree 3 on θ (2,1,2). In this paper we show that the maximum signless Laplacian spectral radii are achieved uniquely by Un3 and θn∗ among all complements of unicyclic graphs and bicyclic graphs of order n, respectively.