# 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.*

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Copyright (c) 2024 Putri Wulandari, Vika Yugi Kurniawan, Nughthoh Arfawi Kurdhi

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