On H-antimagic decomposition of toroidal grids and triangulations

Abstract

Let 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 such that for all subgraphs isomorphic to H in 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 a and the common difference d. When 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.

Keywords

• toroidal grid
• toroidal triangulation
• h-decomposition
• h-supermagic graph
• h-antimagic graph