偶数顶点不含四圈图的无符号拉普拉斯谱半径(英文)  

The signless Laplacian spectral radius of C_4 -free graphs with even order

作　　者：李广斌[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710129

出　　处：《纺织高校基础科学学报》2013年第2期171-175,共5页Basic Sciences Journal of Textile Universities

基　　金：Supported by the National Natural Science Foundation of China(11201374);the Northwestern Poly-technical University Basic Research Foundation(JC201150)

摘　　要：G是一个简单图,矩阵Q(G)=D(G)+A(G)记为图G的无符号拉普拉斯谱半径,其中D(G)和A(G)分别为对角元素为图G顶点度的对角阵和图G的邻接矩阵.本文证明了图G是偶数顶点不含四圈的图,G*是G中有最大无符号拉普拉斯谱半径的图,ρ是G*的无符号拉普拉斯谱半径,则ρ3-ρ2-(n-1)ρ+1-d3u+d2u-∑(du+di)di≤0,对于u∈V(G*).Let G be a simple graph, the matrix Q（G）=D（G）＋A（G） denotes the signless Lapla- cian matrix of G, where D（G） and A（G） denote the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. In this paper, we prove that if G is a C4-free graph （a graph contains no subgraphs isomorphic to C4） with even number n of vertices,G have maximal signless Laplacian spectral radius among all graphs in G, and let p be the spectral radius of its signless Laplacian matrix, thenp3 pz （n-- 1）p＋ 1--d ＋dZ. -- （d. ＋d,）d,0 , for iE N（） u 6 V（G ） .

关 键 词：无符号拉普拉斯 谱半径 不含四圈 

分 类 号：O157.5[理学—数学]