TOTAL NEAR-RING GRAPH

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 allelements of the near-ring N and any two distinct vertices n۱; n۲ ۲ N are adjacentif and only if n۱ + n۲ or n۲ + n۱ ۲ Z(N). We denote total near-ring graph of Nby TN. In this paper we try to give an overview of the structure of TN dependingupon 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 thecase when Z(N) is an ideal and not an ideal of the near-ring N.

کلیدواژه ها:

Near - ring ، right zero-divisors ، right ideal ، diameter ، girth