期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2019
卷号：16
期号：2
页码：163-171
DOI：10.1016/j.akcej.2018.01.008
语种：English
出版社：Elsevier
摘要：AbstractLetLandHbe two simple, nontrivial and undirected graphs. Letobe a vertex ofH, the comb product betweenLandH, denoted byL▹H, is a graph obtained by taking one copy ofLand|V(L)|copies ofHand grafting theith copy ofHat the vertexoto theith vertex ofL. By definition of comb product of two graphs, we can say thatV(L▹H)={(a,v)|a∈V(L),v∈V(H)}and(a,v)(b,w)∈E(L▹H)whenevera=bandvw∈E(H), orab∈E(L)andv=w=o. LetG=L▹HandP2▹H⊆G, the graphGis said to be an(a,d)-P2▹H-antimagic total graph if there exists a bijective functionf:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|}such that for all subgraphs isomorphic toP2▹H, the totalP2▹H-weightsW(P2▹H)=∑v∈V(P2▹H)f(v)+∑e∈E(P2▹H)f(e)form an arithmetic sequence{a,a+d,a+2d,…,a+(n−1)d}, whereaanddare positive integers andnis the number of all subgraphs isomorphic toP2▹H. An(a,d)-P2▹H-antimagic total labelingfis called super if the smallest labels appear in the vertices. In this paper, we study a super(a,d)-P2▹H-antimagic total labeling ofG=L▹HwhenL=Cn.
关键词：KeywordsSuper H-antimagic total labelingComb productCycle graph
