Co-unit graphs associated to ring of integers modulo n

Abstract

Let R be a finite commutative ring. We define a co-unit graph, associated to a ring R, denoted by Gnu(R) with vertex set V(Gnu(R)) = U(R), where U(R) is the set of units of R, and two distinct vertices x, y of U(R) being adjacent if and only if x + y ∉ / U(R). In this paper, we investigate some basic properties of Gnu(R), where R is the ring of integers modulo n, for different values of n. We find the domination number, clique number and the girth of Gnu(R).

Keywords

• unit graph
• co-unit graph
• ring of integers modulo n
• domination number
• 05c50
• 05c12
• 05a18