Neighbourhood $V_4-$magic labeling of some subdivision graphs

Abstract

Let V 4 = {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 V 4-magic if there exists a labeling f : V (G) → V 4 \{0} such that the sum N + f (v) = ∑ u∈N(v) f (u) is a constant map. If this constant is p,where p is any non zero element in V 4 ,then we say that f is a p-neighbourhood V 4-magic labeling of G and G is said to be a p-neighbourhood V 4-magic graph. If this constant is 0,then we say that f is a 0-neighbourhood V 4-magic labeling of G and G is said to be a 0-neighbourhood V 4-magic graph. Keywords Klein-4-group, a-neighbourhood V 4-magic graphs and 0-neighbourhood V 4-magic graphs.