子立方图的严格邻点可区别全染色
Strict Neighbor-Distinguishing Total Coloring of Subcubic Graphs
摘要: 图G的一个正常k-全染色是指一个映射，使得中任意两个相邻的或相关联的元素染不同颜色。令Cφ(v)表示点v的颜色与v的关联边的颜色组成的集合。如果满足对任意一条边都有和，则称φ是k-严格邻点可区别的。图G的严格邻点可区别全色数是使G是k-严格邻点可区别全可染的最小正整数k，用χsnt(G)表示。本文证明了每个子立方图满足。
Abstract: A proper total k-coloring of a graph G is a mapping , such that any two adjacent or incident elements in receive different colors. Let Cφ(v) be the set of colors assigned to a vertex v and those edges incident to v. φ is strict neighbor-distinguishing if and for each edge . The strict neighbor-distin- guishing total index, denoted by χsnt(G), of G is the minimum integer k such that G is k-strict neighbor-distinguishing total colorable. In this paper, we prove that every subcubic graph G has .
文章引用：刘含荃, 顾静. 子立方图的严格邻点可区别全染色[J]. 应用数学进展, 2020, 9(8): 1346-1350. https://doi.org/10.12677/AAM.2020.98159

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