On the Total Neighbor Sum Distinguishing Index of IC-Planar Graphs

被引：2

作者：

Zhang, Donghan ^{[1
]}

Li, Chao ^{[1
]}

Chao, Fugang ^{[1
]}

机构：

[1] Shangluo Univ, Sch Math & Comp Applicat, Shangluo 726000, Peoples R China

来源：

SYMMETRY-BASEL | 2021年 / 13卷 / 10期

关键词：

combinatorial nullstellensatz; IC-planar graphs; total neighbor sum distinguishing coloring; discharging; DISTINGUISHING TOTAL COLORINGS; TOTAL CHROMATIC NUMBER;

D O I：

10.3390/sym13101787

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

A proper total k-coloring f of G with n-ary sumation (z & ISIN;EG(u)?{u})f(z)& NOTEQUAL; n-ary sumation( z & ISIN;EG(v)?{v})f(z) for each uv & ISIN;E(G) is called a total neighbor sum distinguishing k-coloring, where E-G(u)={uv|uv & ISIN;E(G)}. Pilsniak and Wozniak conjectured that every graph with maximum degree & UDelta; exists a total neighbor sum distinguishing (& UDelta;+3)-coloring. In this paper, we proved that any IC-planar graph with & UDelta;& GE;12 satisfies this conjecture, which improves the result of Song and Xu.</p>

引用

页数：13

共 13 条

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