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

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 ξ : V ( G ) ∪ E ( G ) → { 1 , 2 , … , | V ( G ) | + | E ( G ) | } , 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 + 2 d, …, 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 C m ◊ P n with H is P 2 ◊ P n and super ( a, d )- P 2 ◊ C n -antimagic total labeling of C m ◊ C n .