Neighbourhood V₄–magic labeling of some star and path related graphs

Abstract

Let V₄ = {0, a, b, c} be the Klein-4-group with identity element 0. A graph G = (V(G), E(G)) with vertex set V(G) and edge set E(G), is said to be Neighbourhood V₄-magic if there exists a labeling f : V(G) → V₄\{0} such that the sum is a constant map. If this constant is p, where p is any non zero element in V₄, then we say that f is a p-neighbourhood V₄-magic labeling of G and G is said to be a p-neighbourhood V₄-magic graph. If this constant is 0, then we say that f is a 0-neighbourhood V₄-magic labeling of G and G is said to be a 0-neighbourhood V₄-magic graph. In this paper we study Neighbourhood V₄-magic labeling of some star and path related graphs.

Subject Classification:

• 05C78
• 05C25

Keywords:

• Klein-4-group
• a-neighbourhood V₄-magic graphs and 0-neighbourhood V₄-magic graphs