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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Ayunda Faizatul Musyarrofah
Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang
Mathematics

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Some Properties of Prime Graph of Cartesian Product of The Rings and It's Line Graph Vira Hari Krisnawati; Ayunda Faizatul Musyarrofah; Noor Hidayat; Farah Maulidya Fatimah
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.32154

Abstract

The prime graph of the ring R, P G(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 rings Zp1 × Zp2 for distinct prime numbers p1 and p2. We find that some properties of P G(Zp1 × Zp2 ) such as order, size, the number of triangles, and Wiener index. Further, we construct the line graph of P G(Zp1 × Zp2 ) and calculate the order, size, and Wiener index of L(P G(Zp1 × Zp2 )).
Co-Authors Farah Maulidya Fatimah Noor Hidayat Vira Hari Krisnawati