每个点的度数被3整除的生成母图  

The Spanning Supergraphs with the Degree of Each Vertex Divisible by 3

作　　者：熊玮[1] 张启慧 XIONG Wei;ZHANG Qihui(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）（中英文）》2021年第6期665-669,共5页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金项目(11861066,11961067,12001465,61963033).

摘　　要：对于一个简单图G,如果V(G′)=V(G),E(G′)■E(G),就称G′是G的生成母图.顶点v■V(G),图G中与点v关联的边数称为点v的度.本文主要研究简单图G是否存在度能被3整除的生成母图,完全刻画了路图、星图和双星图度能被3整除的生成母图,对于一般图和树图讨论了其有度能被3整除的生成母图的充分条件.For a simple graph G,a graph G′is a spanning supergraph of G,if V(G′)=V(G),E(G′)¶E(G).The degree dG(v)of a vertex v in G is the number of edges of G incident with v.In this paper,we study the problem that simple graphs have spanning supergraphs with the degree of each vertex divisible by 3.We completely characterize the spanning supergraphs of path graphs,star graphs and binary star graphs whose degree can be divided by 3.For general graph and tree graph,we give the sufficient conditions for the spanning supergraphs in which the degree of each vertex can be divided by 3.

关 键 词：生成母图 度能被3整除 树图 

分 类 号：O157.5[理学—数学]