A Note on the Signless Laplacian Spectral Ordering of Graphs with Given Size  

作　　者：Nannan LIU Shuguang GUO 

机构地区：[1]School of Mathematics and Statistics,Qinghai Normal University,Qinghai 810008,P.R.China [2]School of Mathematics and Statistics,Yancheng Teachers University,Jiangsu 224002,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第3期304-312,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 Nos.12071411,12171222)。

摘　　要：Abstract For a simple undirected graph G with fixed size m≥2k(k∈Z^(+))and maximum degree Δ(G)≤m-k,we give an upper bound on the signless Laplacian spectral radius q(G)of G.For two connected graphs G_(1) and G_(2) with size m≥8,employing this upper bound,we prove that q(G_(1))>q(G_(2))if Δ(G_(1))>Δ(G_(2))+1 and Δ(G_(1))≥m/2+2.For triangle-free graphs,we prove two stronger results.As an application,we completely characterize the graph with maximal signless Laplacian spectral radius among all graphs with size m and circumference c for m≥max{2c,c+9},which partially answers the question proposed by Chen et al.in[Linear Algebra Appl.,2022,645:123–136].

关 键 词：signless Laplacian spectral radius upper bound ORDERING SIZE CIRCUMFERENCE 

分 类 号：O157.5[理学—数学]