Strict Neighbor-Distinguishing Total Index of Graphs

• 作者: Jing GU Wei Fan WANG Yi Qiao WANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（4）
• 页码范围: 770-776
• 页数: 7页
• 语种: 英文

摘要

A total-coloring of a graph G is strict neighbor-distinguishing if for any two adjacent vertices u and v,the set of colors used on u and its incident edges and the set of colors used on v and its incident edges are not included with each other.The strict neighbor-distinguishing total index x″snd(G)of G is the minimum number of colors in a strict neighbor-distinguishing total-coloring of G.In this paper,we prove that every simple graph G with Δ(G)≥3 satisfies x″snd(G)≤2Δ(G).