## ON INDEPENEDENCE NUMBER OF NIL GRAPH OF Zn FOR SOME PARTICULAR VALUES OF n

## S. Begum and K. Patra

DOI: https://doi.org/10.37418/amsj.9.11.11

Abstract

Let $R$ be a commutative ring. P.W. Chen [1] defined a kind of graph structure by considering the elements of $R$ as the vertices of the graph. Any two elements $x,y\in R$ are adjacent if $xy\in N(R$), where $N(R)$ denotes the set of nil elements of $R$. This definition was modified by A.H.Li and Q.S.Li [4] by considering the vertex set to be $R-\{0\}$. In our paper we adopt the modified definition given by A.H.Li and Q.S.Li. We call this graph as Nil Graph and determine the independence number of the nil graph $\Gamma_N (\Z_n )$, for some particular values of $n$.

**Keywords: **Nil Graph, Independence Number, Vertex connectivity.