**Journal of Prime Research in Mathematics**

Vol. 18 (2022), Issue 1, pp. 18 – 27

ISSN: 1817-3462E (Online) 1818-5495 (Print)

ISSN: 1817-3462E (Online) 1818-5495 (Print)

# On Metric Dimension of Chemical Networks

**Muhammad Hussain\(^{a,*}\), Saqib Nazeer\(^b\), Hassan Raza\(^c\)**

\(^a\)Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan.

\(^b\)Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan.

\(^c\)Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan.

Correspondence should be addressed to: mmaths@gmail.com

Copyright © 2022 Muhammad Hussain, Saqib Nazeer, Hassan Raza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Published:**Received: : 20 April 2021; Accepted: 30 May 2022; Published Online: 7 June 2022.

### Abstract

Metric Dimension of any graph G is termed as the minimum number of basis element in the resolving set. Let G = (V, E) be any connected graph and length of the shortest path between s and h is known as distance, denoted by d(s, h) in G. Let B = {b1, b2, …, bq} be any ordered subset of V and representation r(u|B) with respect to B is the q−tuple (d(u, b1), d(u, b2), d(u, b3), …, d(u, bq)}, here B is called the resolving set or the locating set if every vertex of G is uniquely represented by distances from the vertices of B or if distinct vertices of G have distinct representations with respect to B. Any resolving set containing minimum cardinality is named as basis for G and its cardinality is the metric dimension of G is denoted by dim(G). We investigated metric dimension of Polythiophene Network, Backbone Network, Hex-derive Network and Nylone6,6.

#### Keywords:

Graphs, Distance, Resolving sets, Metric dimension, Chemical network.