Clique and Independence Number of Rough Co-Zero Divisor Graph and Its Applications in Analyzing a Twitter Data

Abstract

In view of this paper, we have defined Rough Co-zero divisor graph [Formula: see text] of a rough semiring [Formula: see text] for a given approximation space [Formula: see text] where [Formula: see text] is nonempty finite set of objects and [Formula: see text] is an arbitrary equivalence relation on [Formula: see text]. It is proved that the Rough Co-zero divisor graph and the subgraph of Rough Ideal-based rough edge Cayley graph [Formula: see text] are complement to each other. Also the Clique number and Independence number of [Formula: see text] and [Formula: see text] are obtained. The developed concepts are illustrated with suitable examples. A sentiment analysis is also made using [Formula: see text] for a Twitter data.