Non-comaximal graph of ideals of a ring

Let R be a ring. The non-comaximal graph of R, denoted by NC(R) is an undirected graph whose vertex set is the collection of all non-trivial (left) ideals of R and any two distinct vertices I and J are adjacent if and only if \(I+J\ne R\). The concepts of connectedness, independent set, clique and traversability of NC(R) are discussed.