Some Properties of Prime Graph of Cartesian Product of the Ring

CAUCHY Jurnal Matematika Murni dan Aplikasi 2026 Open access

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Authors: Vira Hari Krisnawati, Ayunda Faizatul Musyarrofah, Noor Hidayat, Farah Maulidya Fatimah
DOI: 10.18860/cauchy.v11i1.32154
Cited by: 0

Abstract

The prime graph of the ring R, (PG(R)) is a graph which set of vertices consists of elements of R and two different vertices are adjacent if their product in the ring is zero. We study the prime graph of cartesian product of the ring Z_(p_1 )×Z_(p_2 ) for distinct prime numbers p_1 and p_2. We find that some properties of PG(Z_(p_1 )×Z_(p_2 ) ) such as order, size, the number of triangles, and Wiener. Further, we construct the line graph of PG(Z_(p_1 )×Z_(p_2 ) ) and calculate the order, size, and Wiener index of L(PG(Z_(p_1 )×Z_(p_2 ) )).

Fields of Study & Subjects

Rings Modules and Algebras Graph theory and applications Finite Group Theory Research

Publication details

Journal / source
CAUCHY Jurnal Matematika Murni dan Aplikasi
Volume
11
Issue
1
Pages
255–265
Publication date
5 February 2026
Language
EN