广义Halin图的列表邻和可区别全染色  

List neighbor sum distinguishing total coloring of generalized Halin graphs

作　　者：姚玉亭 唐云芳 YAO Yuting;TANG Yunfang(College of Sciences,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学理学院,浙江杭州310018

出　　处：《中国计量大学学报》2024年第4期684-691,共8页Journal of China University of Metrology

基　　金：国家自然科学基金项目(No.11701543)。

摘　　要：目的:研究广义Halin图的列表邻和可区别全染色。方法:主要利用数学归纳法和组合零点定理进行推导证明。结果:1)若G是最大度Δ≥3的广义Halin图,则ch″∑(G)≤Δ+3,Δ=3;Δ+2,Δ≥4。2)设GΔΔ是含有两个相邻最大度为Δ点的广义Halin图,且WΔ是最大度为Δ的轮图,则ch″∑(G)=Δ+2,G∈{W_(3)}∪{GΔΔ:Δ≥5};Δ+1,G∈{WΔ:Δ≥4}。结论:证明了列表邻和可区别全染色猜想对广义的Halin图成立,并且改进和推广了已知的结果。Aims:This paper aims to study the list neighbor sum distinguishing total coloring of the generalized Halin graphs.Methods:The methods of mathematical induction and combinatorial nullstellensatz were used to deduce and prove the results.Results:1)If G is a generalized Halin graph with maximum degreeΔ≥3,then ch″∑(G)≤Δ+3,Δ=3;Δ+2,Δ≥4.2)Let GΔΔbe a generalized Halin graph with two adjacent vertices of maximum degreeΔ,and WΔbe a wheel graph with maximum degreeΔ,then ch″∑(G)=Δ+2,G∈{W_(3)}∪{GΔΔ:Δ≥5};Δ+1,G∈{WΔ:Δ≥4}.Conclusions:It shows that the list version conjecture of the neighbor sum distinguishing total coloring holds for generalized Halin graphs.It improves and extends the known results.

关 键 词：广义Halin图 轮图 列表邻和可区别全染色 组合零点定理 

分 类 号：O157.5[理学—数学]