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_ (p₁) ×Z_ (p₂) for distinct prime numbers p₁ and p₂. We find that some properties of PG (Z_ (p₁) ×Z_ (p₂) ) such as order, size, the number of triangles, and Wiener. Further, we construct the line graph of PG (Z_ (p₁) ×Z_ (p₂) ) and calculate the order, size, and Wiener index of L (PG (Z_ (p₁) ×Z_ (p₂) ) ).
Krisnawati et al. (Thu,) studied this question.