Unit Graph of the Ring Zₘₙ

Let R be a commutative ring with unity and $$U(R)$$ be the set of all units of R . The unit graph of R, denoted by $$G(R)$$ , is the (undirected) graph with vertex set R and two distinct vertices x and y in $$G(R)$$ are adjacent if and only if $$x+y$$ ∈ $$U(R)$$ . In this paper, we investigate certain fundamental properties of the unit graph of Zₘ × Zₙ , where $$m,n>1$$ be any two integers. We also give the traversability properties of the unit graph of Zₘₙ . Further, we determine the clique number, the chromatic number, the independent number, and the covering number of the unit graph of Zₘₙ .