Maxima of the Q-Index for Halin Graphs  

作　　者：Qi KONG Ligong WANG Yong LU 

机构地区：[1]Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Shaanxi 710072, P. R. China

出　　处：《Journal of Mathematical Research with Applications》2017年第3期253-261,共9页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11171273);the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(Grant No.Z2016170)

摘　　要：The Q-index of a graph G is the largest eigenvalue q（G） of its signless Laplacian matrix Q（G）. In this paper, we prove that the wheel graph W_n = K_1 ∨C_（n-1）is the unique graph with maximal Q-index among all Halin graphs of order n. Also we obtain the unique graph with second maximal Q-index among all Halin graphs of order n.The Q-index of a graph G is the largest eigenvalue q（G） of its signless Laplacian matrix Q（G）. In this paper, we prove that the wheel graph W_n = K_1 ∨C_（n-1）is the unique graph with maximal Q-index among all Halin graphs of order n. Also we obtain the unique graph with second maximal Q-index among all Halin graphs of order n.

关 键 词：Halin graph signless Laplacian spectral radius wheel graph 

分 类 号：O157.5[理学—数学] O171[理学—基础数学]