基于推理反证法的轮图集边控制问题研究  

Research on Set Edge Domatic Problem of Wheel Graphs Based on Deductive Reduction Method

作　　者：徐保根 郑萌萌 兰婷 Xu Baogen;Zheng Mengmeng;Lan Ting(School of Science,East China Jiao tong University,Nanchang 330013,China)

机构地区：[1]华东交通大学理学院,江西南昌330013

出　　处：《华东交通大学学报》2022年第6期112-120,共9页Journal of East China Jiaotong University

基　　金：国家自然科学基金项目(11961026);江西省高校科技落地计划项目(KJLD12067);江西省自然科学基金项目(20171BAB201009,20181BAB201002)。

摘　　要：随着控制理论的快速发展,有关图的边控制集划分问题备受人们关注。对于非空图G=(V,E),D■E,若V_(e)∈E-D,都存在e′∈D,使得e与e′相邻,则可称D为图G的一个边控制集。E(G)是图G的所有边组成的集合,E(G)所能划分成的互不相交的边控制集的最多数目就是图G的集边控制数d′(G)。主要研究了具有强对称性的轮图W_(n+1)的边控制集划分问题,并且通过推理反证法来寻找标号规律,最终获得了轮图W_(n+1)的集边控制数,从而实现了推理反证法在特殊图边控制集划分问题中的应用。With the rapid development of domination theory,the problem of edge domatic set partition of graphs has attracted much attention.As G=(V,E),a nonempty graph,D■E is said to be an edge domination set of G.If Ve ■ E-D,there exists an edge e′■ D,so that e ′is adjacent to ef and E(G)is the set of all the edges of G.The maximum number of nonintersecting edge domination sets that can be partitioned into is the edge domatic number d′(G)of graph G.The partition of edge domination set of Wheel graph W_(n+1) with strong symmetry is the main research content,and the set edge domination number of Wheel graph W_(n+1) is obtained by deductive reduction method.Accordingly,the application of deductive reduction method in edge domatic set partition of special graph is realized.

关 键 词：边控制集 集边控制数 图 轮图 

分 类 号：O157.5[理学—数学]