围长至少为5的IC-可平面图的邻点可区别边染色  

Adjacent Vertex Distinguishing Edge Coloring of IC-planar Graphs with Girth at Least 5

作　　者：杨腾飞 徐常青[1] YANG Teng-fei;XU Chang-qing(School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《数学的实践与认识》2022年第10期179-183,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12071260,12001154);国家自然科学基金中韩项目(1211101361);河北省自然科学基金青年基金项目(A2021202025)。

摘　　要：给图G一个正常k-边染色φ,对G的任意两个相邻的顶点u和v,若满足与u关联的边所染颜色集合和与v关联的边所染颜色的集合不同,则称φ为图G的k-邻点可区别边染色.用χ′_(a)(G)表示图G的邻点可区别边色数,即使得G有一个k-邻点可区别边染色的最小正整数k.通过运用权转移方法研究围长至少为5的正常IC-可平面图的邻点可区别边染色,得到了χ′_(a)(G)≤max{△(G)+2,11}.Given a proper k-edge coloring φ of graph G such that any pair of adjacent vertices u and v,the color set of edges incident with u is different from the color set of edges incident with v,then φ is called a k-adjacent vertex distinguishing edge coloring of graph G.The adjacent vertex distinguishing chromatic number of a graph G refers to the smallest positive integer k that makes G have a k-adjacent vertex distinguishing edge coloring,denoted by χ′_(a)(G).By using the discharging method to study the adjacent vertex distinguishing edge coloring of a normal IC-planar graph G with girth at least 5,we get χ′_(a)(G)≤max{△(G)+2,11}.

关 键 词：IC-可平面图 邻点可区别边染色 权转移方法 

分 类 号：O157.5[理学—数学]