A special research on homo cordial labeling of spider graph

Abstract

Let G= (V, E) be a graph with p vertices and q edges. A Homo Cordial Labeling of a graph G with vertex set V is a bijection from V to {0, 1} such that each edge uv is assigned the label 1 if f(u)=f(v) or 0 if f (u) ≠ f (v) with the condition that the number of vertices labelled with 0 and the number of vertices labelled with 1 differ by at most 1 and the number of edges labelled with 0 and the number of edges labelled with 1 differ by at most 1. The graph that admits a Homo- Cordial labelling is called Homo Cordial graph. In this paper we prove that the spider graph SP(1m, 2t) is Homo-Cordial labelling graph and further study on the generalisation of labelling spider graph SP(1m, 2t).