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TOTAL NEAR-RING GRAPH
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DOI：10.22044/JAS.2024.13537.1753.png)
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Abstract
En 中文
. Let N be a right near-ring and Z(N) be the set of right zero-divisors of N. We define 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 E N are adjacent if and only if n1 + n2 or n2 + n1 E 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 all right zero-divisors Z(N) is an ideal of N or not. We also find 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.
Keywords:
Near-ring
Right zero-divisors
Right ideal
Connected graph
Diameter
Girth