-super antimagic total labeling of comb product of graphs. Issue 2 (1st August 2019)

• Record Type: Journal Article
• Authors: Agustin, Ika Hesti; Prihandini, R.M.; Dafik,
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 16:Issue 2(2019)
• Page Start: 163
• Page End: 171
• Publication Date: 2019-08-01
• Subjects: Super H-antimagic total labeling -- Comb product -- Cycle graph
• DOI: 10.1016/j.akcej.2018.01.008
• Languages: English
• ISSNs: 0972-8600

Abstract

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 .