Abstract
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.