Some Properties of Prime Graph of Cartesian Product of the Ring

Vira Hari Krisnawati, Ayunda Faizatul Musyarrofah, Noor Hidayat, Farah Maulidya Fatimah

Abstract


The prime graph of the ring R, PG(R), is a graph whose set of vertices consists of elements of R, and two distinct vertices are adjacent if their product in the ring is zero. In this paper, we study the prime graph of the Cartesian product of rings Zp1 × Zp2, where p1 and p2 are distinct prime numbers. We determine several properties of PG(Zp1 × Zp2), including its order, size, number of triangles, and Wiener index. Furthermore, we construct the line graph of PG(Zp1 × Zp2) and compute the order, size, and Wiener index of L(PG(Zp1 × Zp2)).


Keywords


Prime graph of a ring, Cartesian product, Triangles, Line graph, Wiener index

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DOI: https://doi.org/10.18860/cauchy.v11i1.32154

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