Super (a, d)-H-antimagic total labeling of edge corona product on cycle with path graph and cycle with cycle graph

Abstract

A simple graph G = (V(G), E(G)) admits a H-covering, where H is subgraph of G, if every edge in E(G) belongs to a subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G 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 + (k – 1)d where a and d are positive integers and k is the number of subgraphs of G isomorphic to H. Such a labeling is called super if the smallest possible labels appear on the vertices. This research has found super (a, d)-H-antimagic total labeling of edge corona product of cycle and path denoted by Cm ◊ Pn with H is P2 ◊ Pn and super (a, d)-P2 ◊ Cn-antimagic total labeling of Cm ◊ Cn.