Some Convex Polytopes Joining Paths and Their Metric Dimension

In recent years, there is a lot of interest in the topic of conveying the groups of planar graphs with an unvarying metric dimension. A few types of planar graphs have recently had their locating number (or metric dimension) determined, and an outstanding problem concerning these graphs was brought up that: Illustrate the types of planar graphs Υ that can be generated from a graph Φ through the addition of more edges to Φ , such that d i m ( Φ ) = d i m ( Υ ) and V ( Φ ) = V ( Υ ) . While proceeding in a similar directives, we identify two families of radially identical planar graphs with unaltered metric dimension in this study: ϝ n , m and ℷ n , m . We do this by establishing that d i m ( ϝ n , m ) = d i m ( ℷ n , m ) and V ( ϝ n , m ) = V ( ℷ n , m ) , respectively. We acquire another family of a radially symmetrical plane graph (i.e., ℸ n , m ) with a constant metric dimension. We show that all the vertices of these classes of the plane graphs can potentially be identified with just three well-chosen nodes.