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On H-antimagic decomposition of toroidal grids and triangulations

Abstract:

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