@ARTICLE{10.3389/fphy.2021.749166,
AUTHOR={Sharma, Sunny Kumar and Raza, Hassan and Bhat, Vijay Kumar},
TITLE={Computing Edge Metric Dimension of One-Pentagonal Carbon Nanocone},
JOURNAL={Frontiers in Physics},
VOLUME={9},
YEAR={2021},
URL={https://www.frontiersin.org/articles/10.3389/fphy.2021.749166},
DOI={10.3389/fphy.2021.749166},
ISSN={2296-424X},
ABSTRACT={Minimum resolving sets (edge or vertex) have become an integral part of 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 (distinguishes) two edges e_{1} and e_{2} in a connected graph G. A subset of vertices R_{E} 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 u ∈ R_{E}. 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.}
}