# ON PROPERTIES OF PRIME IDEAL GRAPHS OF COMMUTATIVE RINGS

• Rian Kurnia Mathematics Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
• Ahmad Muchlas Abrar Mathematics Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
• Abdul Gazir Syarifudin Mathematics Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
• Verrel Rievaldo Wijaya Mathematics Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
• Nur Ain Supu Mathematics Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
• Erma Suwastika Mathematics Department, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Indonesia
Keywords: Prime ideal graph, Commutative ring, Independence number, Metric and local metric dimension, Partition dimension, Clique and Independence number, Topological indices

### Abstract

The prime ideal graph of  in a finite commutative ring  with unity, denoted by , is a graph with elements of  as its vertices and two elements in  are adjacent if their product is in . In this paper, we explore some interesting properties of . We determined some properties of  such as radius, diameter, degree of vertex, girth, clique number, chromatic number, independence number, and domination number. In addition to these properties, we study dimensions of prime ideal graphs, including metric dimension, local metric dimension, and partition dimension; furthermore, we examined topological indices such as atom bond connectivity index, Balaban index, Szeged index, and edge-Szeged index.

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Published
2023-09-30
How to Cite
[1]
R. Kurnia, A. Abrar, A. Syarifudin, V. Wijaya, N. Supu, and E. Suwastika, “ON PROPERTIES OF PRIME IDEAL GRAPHS OF COMMUTATIVE RINGS”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1463-1472, Sep. 2023.
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Articles