(a, d)-H-Anti Magic Total Labeling on Double Cones Graph

Abstract

A simple graph G = (V (G), E(G)) admits an H-covering if every edge in E(G) belongs to a subgraph of G that is isomorphic to H and there is a bijective function such that for all subgraphs H’ isomorphic to H, the H-weights w(H’) = ∑v∈V (H’) ξ(v) + ∑e∈E(H’) ξ(e) constitute an arithmetic progression a, a + d, a + 2d, …, a + (t − 1)d where a and d are positive integers and t is the number of subgraphs of G isomorphic to H. The labeling ξ is called a super (a, d)-H-anti magic total labeling, if ξ (V(G)) = {1, 2, …, |V (G)|}. The aim of this research is to find some (a, d)-H-anti magic total labelings on double cones graph.