On H -antimagicness of Cartesian product of graphs

A graph G = (V (G), E(G)) admits an H -covering if every edge in E belongs to a subgraph of G isomorphic to H . A graph G admitting an H -covering is called (a, d) -H -antimagic if there is a bijection f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that, for all subgraphs H ′ of G isomorphic to H , the H -weights, wtf (H ′) = ∑ v∈V (H′) f(v)+ ∑ e∈E(H′) f(e), constitute an arithmetic progression with the initial term a and the common difference d . In this paper we provide some sufficient conditions for the Cartesian product of graphs to be H -antimagic. We use partitions subsets of integers for describing desired H -antimagic labelings.