-super antimagic total labeling of comb product of graphs

Abstract

Let and be two simple, nontrivial and undirected graphs. Let be a vertex of , the comb product between and , denoted by , is a graph obtained by taking one copy of and copies of and grafting the th copy of at the vertex to the th vertex of . By definition of comb product of two graphs, we can say that and whenever and , or and . Let and , the graph is said to be an --antimagic total graph if there exists a bijective function such that for all subgraphs isomorphic to , the total -weights form an arithmetic sequence , where and are positive integers and is the number of all subgraphs isomorphic to . An --antimagic total labeling is called super if the smallest labels appear in the vertices. In this paper, we study a super --antimagic total labeling of when .

Keywords

• super h-antimagic total labeling
• comb product
• cycle graph