华东师范大学学报（自然科学版）Issue(2)：14-22,9.DOI:10.3969/j.issn.1000-5641.2024.02.002
圈与路的点被多重集可区别的E-全染色
E-total coloring of cycles and paths which are vertex-distinguished by multiple sets
摘要
Abstract
An E-total coloring of a graph G is an assignment of several colors to all vertices and edges of G such that no two adjacent vertices receive the same color and no edge receive the same color as one of its endpoints.If f is an E-total coloring of a graph G,the multiple color set of a vertex x of G under f is the multiple set composed of colors of x and the edges incident with x.If any two distinct vertices of G have distinct multiple color sets under an E-total coloring f of a graph G,then f is called an E-total coloring of G vertex-distinguished by multiple sets.An E-total chromatic number of G vertex-distinguished by multiple sets is the minimum number of the colors required in an E-total coloring of G vertex-distinguished by multiple sets.The E-total colorings of cycles and paths vertex-distinguished by multiple sets are discussed by use of the method of contradiction and the construction of concrete coloring.The optimal E-total colorings of cycles and paths vertex-distinguished by multiple sets are given and the E-total chromatic numbers of cycles and paths vertex-distinguished by multiple sets are determined in this paper.关键词
圈/路/多重色集合/E-全染色/点被多重集可区别的E-全染色Key words
cycle/path/multiple color set/E-total coloring/E-total coloring vertex-distinguished by multiple sets分类
数理科学引用本文复制引用
陈祥恩,曹静..圈与路的点被多重集可区别的E-全染色[J].华东师范大学学报（自然科学版）,2024,(2):14-22,9.基金项目
国家自然科学基金(11761064) （11761064）
