Some Properties of Cartesian Product of Non-Coprime Graph Associated with Finite Group - Bawana, Agista Surya; Qonita, Niswah; Syarifudin, Abdul Gazir; Susanti, Yeni (IndoMS, 2025)
This paper investigates several properties of the Cartesian product of two non-coprime graphs associated with finite groups. Specifically, we focus on key numerical invariants, namely the domination number, independence number, and diameter. The non-coprime graph associated with finite group G is constructed with the vertex set G{e} and connects two distinct vertices if and only if their orders are not coprime. Using this construction, we investigate the Cartesian products of non-coprime graphs associated with various types of groups, including nilpotent groups, dihedral groups, and p-groups. We derive several new results, including exact expressions for the domination number, independence number, and diameter of these Cartesian products.