Co-unit graphs associated to ring of integers modulo n

This is the authors' abstract. We don't add key points for this paper.

Let R be a finite commutative ring. We define a co-unit graph, associated to a ring R , denoted by G nu ( R ) with vertex set V ( G nu ( 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 G nu ( 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 G nu ( R ).