Computing Some Resolvability Parameters for Two-Fold Circular Ladder

Let [Formula: see text] be an undirected, planar, non-trivial, connected, and simple graph, where the sets [Formula: see text] and [Formula: see text] are respectively the vertex and edge sets for [Formula: see text]. The cardinalities of the sets [Formula: see text] and [Formula: see text] (i.e., [Formula: see text] and [Formula: see text]) are referred to be the size and order of [Formula: see text]. A subset [Formula: see text] (ordered vertices) of [Formula: see text] is termed as a resolving set [edge resolving set (ERS)] for [Formula: see text] if for every two distinct vertices [Formula: see text] [edges [Formula: see text]], there is a vertex [Formula: see text] such that [Formula: see text] [[Formula: see text]]. A resolving set (ERS) consisting of the minimum number of vertices is called the metric basis [edge metric basis (EMB)] for [Formula: see text] and the cardinality of metric basis (EMB) set is its metric dimension (edge metric dimension), represented by [Formula: see text] [[Formula: see text]]. In this paper, we initiate the study of edge and vertex resolvability parameters for a novel class of planar graphs. Further, we will show that the planar graph possesses an independent minimum vertex and the edge resolving sets having cardinality 3 or 4.