Nonlocal Edge Metric Dimension on Corona Multiproduct Graphs

The nonlocal metric dimension of a graph \(G\), denoted \({{\text{dim}}}_{{\text{nl}}}\left(G\right)\) is known as the cardinality of the smallest nonlocal resolving set \(W\) in \(G\). \(W\) resolve any vertices \(u\) and \(v\) that are not adjacent in G based on the distance from \(u\) and \(v\) to each vertex in \(W\). In this study, a subset of vertices \({W}_{E}\) is called a nonlocal edge resolving set in \(G\) if \({W}_{E}\) resolve any two edges \({e}_{i}\) and \({e}_{j}\) in \(G\) where both are not adjacent. Thus, \({e}_{i}\) and \({e}_{j}\) have different representations to \({W}_{E}\). The cardinality of minimum \({W}_{E}\) is called the nonlocal edge metric dimension and is denoted by \({{\text{edim}}}_{{\text{nl}}}\left(G\right)\). The purpose of this study is to introduce the concept of nonlocal edge metric dimensions and further analyze graphs with certain neighboring characteristics. In this study, a multiproduct corona graph \(G{\odot }^{k}H\) was used. The graph \(G{\odot }^{k}H\) was obtained from \((G{\odot }^{k-1}H)\odot H\). The research was conducted by reviewing the literature and constructing several multiproduct corona graphs for analysis of nonlocal edge metric dimension value patterns. The output of this research is getting the form of new characteristics and theorems regarding metric dimensions of nonlocal edges, especially in multiproduct corona graphs.