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.
|Journal||AKCE International Journal of Graphs and Combinatorics|
|Publication status||Accepted/In press - 2020|
- H-antimagic graph
- H-supermagic graph
- Toroidal grid
- toroidal triangulation