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

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 )).

Keywords


Prime Graph; Cartesian Product of Rings; Line Graph; Wiener Index.

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

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