厦门大学学报（自然科学版）2025，Vol.64Issue(6)：1005-1010,6.DOI:10.6043/j.issn.0438-0479.202410023
3≤Δ≤4的图的D(2)-点和可区别全染色
The D(2)-vertex sum distinguishing total coloring of graphs with 3≤Δ≤4
摘要
Abstract
[Objective]This study explores characteristics of D(2)-vertex sum distinguishing total coloring for simple connected graphs G with maximum degree satisfying 3≤Δ≤4,clarifies their vertex sum distinguishing total chromatic numbers,and further extends the research conclusions of this coloring problem to planar graphs,thereby providing the support for the improvement of relevant coloring theories in graph theory.[Methods]We conduct a combined research approach of the Combinatorial Nullstellensatz and the method of weight transfer.The Combinatorial Nullstellensatz is used to establish the theoretical basis for the existence of coloring,while the discharging method is employed to analyze the weight distribution relationship between vertices and edges in the graph,so that the rationality and the feasibility of the coloring scheme are verified.[Results]The specific value of the D(2)-vertex sum distinguishing total chromatic number for simple connected graphs G with 3≤Δ≤4 is successfully determined.Furthermore,this conclusion is extended to the category of planar graphs,and it is proved that planar graphs satisfying3≤Δ≤4also possess the corresponding D(2)-vertex sum distinguishing total coloring property,with their vertex sum distinguishing total chromatic numbers being consistent with those of simple connected graphs.[Conclusions]The Combinatorial Nullstellensatz and the discharging method can effectively solve the D(2)-vertex sum distinguishing total coloring problem for graph classes with 3≤Δ≤4.These obtained chromatic-number conclusions are applicable to both simple connected graphs and planar graphs,thus providing referable methodological and theoretical bases for subsequent research on such chromatic number problems within other ranges.关键词
D(2)-点和可区别全染色/组合零点定理/权转移方法Key words
D(2)-vertex sum distinguishing total colorings/combinatorial nullstellensatz/discharging method分类
数理科学引用本文复制引用
何静,强会英..3≤Δ≤4的图的D(2)-点和可区别全染色[J].厦门大学学报（自然科学版）,2025,64(6):1005-1010,6.基金项目
国家自然科学基金(61962035) （61962035）
