Metric basis and metric dimension of 1-pentagonal carbon nanocone networks
Zafar Hussain, Mobeen Munir, Ashfaq Ahmad, Maqbool Ahmad Chaudhary, Junaid Khan, Imtiaz Ahmed
Abstract
Resolving set and metric basis has become an integral part in combinatorial chemistry and molecular topology. It has a lot of applications in computer, chemistry, pharmacy and mathematical disciplines. A subset S of the vertex set V of a connected graph G resolves G if all vertices of G have different representations with respect to S. A metric basis for G is a resolving set having minimum cardinal number and this cardinal number is called the metric dimension of G. In present work, we find a metric basis and also metric dimension of 1-pentagonal carbon nanocones. We conclude that only three vertices are minimal requirement for the unique identification of all vertices in this network.