Total near - ring graph

Document Type : Original Manuscript


Department of Mathematics, Girijananda Chowdhury University. Guwahati.Assam. India



Let N be a right near-ring. Let Z(N) be the set of right zero-divisors of N.
We de ne total near-ring graph of N as a graph whose vertex set is the set of all
elements of the near-ring N and any two distinct vertices n1; n2 2 N are adjacent
if and only if n1 + n2 or n2 + n1 2 Z(N). We denote total near-ring graph of N
by TN. In this paper we try to give an overview of the structure of TN depending
upon whether the set of right zero-divisors Z(N) is an ideal of N or not. We also
nd the girth and diameter of TN and its two subgraphs TZ(N) and TReg(N) for the
case when Z(N) is an ideal and not an ideal of the near-ring N.