Neighbourhood distinguishing coloring in graphs

Abstract

In the case of a finite dimensional vector space $V$, any ordered basis can be used to give distinct codes for elements of $V$. Chartrand et al introduced coding for vertices of a finite connected graph using distance. A binary coding of vertices of a graph (connected or disconnected) was suggested by Suganthi. Motivated by these results, a new type of coding, called neighborhood distinguishing coloring code, is introduced in this paper. A study of this code is initiated.