哈密尔顿二次迭代线图的边度条件  

Edge Degree Conditions for Hamiltonian 2-iterated Line Graphs

作　　者：刘泽萌 熊黎明 熊玮[2] LIU Zemeng;XIONG Liming;XIONG Wei(School of Mathematics and Statistics,Beijing Institute of Technology,Beijing,100081,P.R.China;College of Mathematics and System Science,Xinjiang University,Urumqi,Xinjiang,830046,P.R.China)

机构地区：[1]北京理工大学数学与统计学院,北京100081 [2]新疆大学数学与系统科学学院,乌鲁木齐新疆830046

出　　处：《数学进展》2021年第5期793-799,共7页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.11871099,11671037,12001465)。

摘　　要：图G=(V(G),E(G))的线图L(G)是指以G的边集E(G)为顶点集且L(G)的2个顶点相邻当且仅当它们在G中有公共顶点.定义G的最小边度σ_(2)(G)=min{dG(u)+dG(v):uv∈E(G)}.对于连通图G,给出σ_(2)(G)的精确界,使得L(L(G))是哈密尔顿的(即存在支撑圈).对于每一条割边都是悬挂边的连通图H,给出σ_(2)(H)的精确界,使得L(L(H))是哈密尔顿的.The line graph L(G)of G=(V(G),E(G))has E(G)as its vertex set,and two vertices are adjacent in L(G)if and only if the corresponding edges share a common end vertex in G.Let σ_(2)(G)=min{dG(u)+dG(v):uv∈E(G)}.A sharp bound of σ_(2)(G)for a connected graph G such that L(L(G))is Hamiltonian(i.e.,has a spanning cycle)is given.A sharp bound of σ_(2)(H)for a connected graph H in which every cut edge is a pendent edge such that L(L(H))is Hamiltonian is also given.

关 键 词：迭代线图 哈密尔顿指数 边度条件 

分 类 号：O157.5[理学—数学]