OnH-antimagicness of Cartesian product of graphs

Abstract

A graphG= (V(G);E(G)) admits anH-covering if every edge inEbelongs to a subgraph ofGisomorphic toH. A graphGadmitting anH-covering is called (a;d)-H-antimagicif there is a bijectionf:V(G)[E(G)!f1;2;:::;jV(G)j+jE(G)jgsuch that, for all subgraphsH′ofGisomorphic toH, theH-weights,wtf(H′) =∑v2V(H′)f(v)+∑e2E(H′)f(e);constitute an arithmetic progression with the initial termaand the commondifferenced. In this paper we provide some sufficient conditions for the Cartesian product of graphs to beH-antimagic.We use partitions subsets of integers for describing desiredH-antimagic labelings.