Department of Mathematics, Girijananda Chowdhury University. Guwahati.Assam. India
10.22044/jas.2024.13537.1753
Abstract
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.
)