Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone - Sharma, Sunny Kumar; Raza, Hassan; Bhat, Vijay Kumar (Frontiers in Physics, 2021)
Minimum resolving sets (edge or vertex) have become an integral part in molecular topology and combinatorial chemistry. Resolving sets for a specific network provide crucial information required for the identification of each item contained in the network, uniquely. The distance between an edge e=cz and a vertex u is defined by d(e,u)=min{d(c,u), d(z,u)}. If d(e_1,u)≠ d(e_2,u), then we say that the vertex u resolves (or distinguishes) two edges e_1 and e_2 in a connected graph G. A subset of vertices R in G is said to be an edge resolving set for G, if for every two distinct edges e_1 and e_2 in G we have d(e_1,u)≠ d(e_2,u) for at least one vertex uR. An edge metric basis for G is an edge resolving set with minimum cardinality and this cardinality is called the edge metric dimension edim(G) of G. In this article, we determine the edge metric dimension of one-pentagonal carbon nanocone (1-PCNC). We also show that the edge resolving set for 1-PCNC is independent.