CONSTRUCT THE TRIPLE ZERO GRAPH OF RING Z_n USING PYTHON

Abstract

Let be a commutative ring with nonzero identity and there exists such that , , , denotes the set of all triple zero elements of . The triple zero graph of , denoted by , is an undirected graph with vertex set where two distinct vertices and are adjacent if and only if , and there exists a nonzero element of such that , , and . Python is a programming language with simple and easy-to-learn code that can be used to solve problems in algebra and graphs. In this paper, we construct the triple zero graph of ring using Python. Based on the output of the program, several properties of are obtained, such as if and , then is a planar graph, if with is prime numbers, then is a complete graph , and if with is prime numbers and , then is a connected graph.