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On H-antimagicness of Cartesian product of graphs

Abstract:

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) (n-ary union) E(G) → (1; 2,..,|V(G)| + |E(G)|) such that, for all subgraphs H' of G isomorphic to H, the H-weights, wtf (H') =∑ υ∈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.