Non-Conjugate Graphs Associated With Finite Groups

Let $G$ be a finite group and $S$ be a non-empty subset of $G$ comprising of the non-conjugate elements. In this study, we introduced the non-conjugate graph associated with $G$ with a coinciding set of vertices, such that two distinct vertices $x$ and $y$ are adjacent only if $x,y\in S$ . We then discussed some fundamental properties to ensure the algebraic and combinatorial structure of the graph. Afterward, we formulated the resolving set and resolving polynomial for a subclass of dicyclic groups