发表机构
Eötvös Loránd University; Amrita Vishwa Vidyapeetham（罗兰大学; 阿莫瑞塔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对笛卡尔乘积、字典序乘积等多类图乘积，验证了邻点可区别全染色猜想（AVD-TCC）的正确性，拓展了该图论猜想的适用范围。
AI 中文摘要
图G的邻点可区别全（AVD-全）色数χ''_a(G)是使得G存在k色正常全染色f，且对每条边uv∈E(G)满足C_G(u)≠C_G(v)的最小整数，其中C_G(u)={f(u)}∪{f(uw):uw∈E(G)}。邻点可区别全染色猜想（AVD-TCC）断言，对任意简单图G，χ''_a(G)≤Δ(G)+3，Δ(G)为G的最大度。本文证明了若干类图乘积满足AVD-TCC，包括笛卡尔乘积、字典序乘积、斜乘积、覆盖乘积、梳乘积及Indu-Bala乘积。
英文摘要
The adjacent vertex distinguishing (AVD)-total chromatic number $χ''_{a}(G)$ of a graph $G$ is the least integer $k$ for which $G$ has a proper total coloring $f$ with $k$ colors such that $C_G(u)\neq C_G(v)$ for every edge $uv\in E(G)$, where $C_G(u)=\{f(u)\}\cup\{f(uw):uw\in E(G)\}$. The AVD-total coloring conjecture (AVD-TCC) asserts that $χ''_{a}(G)\leq Δ(G)+3$ for every simple graph $G$, where $Δ(G)$ is the maximum degree of $G$. In this paper, we prove the AVD-TCC for certain classes of graph products, including Cartesian products, lexicographic products, skew products, cover products, comb products, and Indu--Bala products.
Comments6 figures, 7 theorems
