Work

Some Properties of Prime Graph of Cartesian Product of the Ring

Year: 2026

Type: article

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 ) )).

Source: CAUCHY Jurnal Matematika Murni dan Aplikasi

DOI: 10.18860/cauchy.v11i1.32154

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

Institution: University of Brawijaya

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $110

OpenAlex ID: W7125932696

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