On H-antimagic decomposition of toroidal grids and triangulations

AbstractLet be a finite simple graph with pvertices and qedges. A decomposition of a graph Ginto isomorphic copies of a graph His called (a, d)-H-antimagic if there is a bijection such that for all subgraphs isomorphic to Hin the decomposition of G, the sum of the labels of all the edges and vertices belonging to constitutes an arithmetic progression with the initial term aand the common difference d. When then Gis said to be super(a, d)-H-antimagic and if d = 0 then Gis called H-supermagic. In the paper we examine the existence of such labelings for toroidal grids and toroidal triangulations.