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 (Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang, 2026)
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 )).