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 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 ) )).

Keywords


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

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References


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

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