Clique Number and Girth of the Rough Ideal-Based Rough Edge Cayley Graph

In this paper, clique number and girth of the rough ideal-based rough edge Cayley graphs [Formula: see text] and [Formula: see text], where [Formula: see text] is the rough Ideal of the rough semiring [Formula: see text] and [Formula: see text] contains the nontrivial elements of [Formula: see text], are evaluated. We prove that the clique number of [Formula: see text] is [Formula: see text] and the clique number of [Formula: see text] is [Formula: see text]. Girth of [Formula: see text] and [Formula: see text] is 3. These concepts are illustrated with examples.