Equivalence Classes and Discernibility in Power Graphs

https://doi.org/10.5281/zenodo.18802166

Abstract

In this paper, we study indiscernibility partitions and cardinality of each indiscernibility partition of power graph of a finite group , where . The emerging theory of rough set is applied on power graph of a finite group  using the concept of open and closed neighborhood. We define the indiscernibility relations in terms of neighborhood and discuss necessary and sufficient conditions for indiscernibility partitions. We study granular computing techniques using information systems. Further, we study rough approximations, rough membership function, discernibility matrix, reduct, core, essential sets and some topological properties.