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 Laplacian 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 ρ be the spectral radius of its signless Laplacian matrix,then ρ3-ρ2-(n-1)ρ + 1-d3u + d2u-∑i∈N(u) (du + di) di ≤ 0,for u ∈ V(G*).
展开▼
