Research Article On the Constant Edge Resolvability of Some Unicyclic and Multicyclic Graphs Dalal Alrowaili , 1 Zohaib Zahid , 2 Imran Siddique , 2 Sohail Zafar, 2 Muhammad Ahsan , 2 and Muhammad Sarwar Sindhu 3 1 Department of Mathematics, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia 2 Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan 3 Department of Mathematics, Virtual University of Pakistan, Lahore 54770, Pakistan Correspondence should be addressed to Imran Siddique; imransmsrazi@gmail.com Received 16 April 2022; Revised 23 June 2022; Accepted 24 June 2022; Published 19 July 2022 Academic Editor: Gohar Ali Copyright © 2022 Dalal Alrowaili et al. is 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. Assume that G (V(G),E(G)) is a connected graph. For a set of vertices W E ⊆V(G), two edges g 1 ,g 2 ∈ E(G) are distinguished by a vertex x 1 ∈ W E , if d(x 1 ,g 1 ) ≠ d(x 1 ,g 2 ). W E is termed edge metric generator for G if any vertex of W E distinguishes every two arbitrarily distinct edges of graph G. Furthermore, the edge metric dimension of G, indicated by edim(G), is the cardinality of the smallest W E for G. e edge metric dimensions of the dragon, kayak paddle, cycle with chord, generalized prism, and necklace graphs are calculated in this article. 1. Introduction and Preliminaries A chemical compound’s structure is typically seen as a col- lection of functional groups arranged on a substructure. e structure is a labeled graph from a graph-theoretic outlook, with the vertex and edge labels indicating the atom and bond types, respectively. Functional groupings and substructure are essentially subgraphs of the labeled graph representation from this perspective. A collection of compounds described by the substructure common to them is fundamentally defined by modifying the set of functional groups and permuting their locations. Chartrand et al. defined chemistry as the appli- cation of graphs to illustrate the structure of diverse chemical compounds (see [1, 2]). We employ graph principles to ex- plain chemical structures in chemical graph theory. Chemical compounds’ atomic structure can be presented using graphs. Johnson has worked on the application of structure-activity relationships by labeled graphs (see [3]). By establishing the concept of metric dimension, Slater was able to locate the invader in a computer network (see [4]). Harary and Melter extended the work of Slater in [5]. Hosamani et al. studied the connection to chemical problems in [6]. Berhe and Wang calculated topological coindices for nanotubes and graphene sheets in [7]. Goyal et al. focused on the new composition of graphs in [8]. Ranjini et al. investigated the applications of molecular topology by degree sequence of graph operator in [9]. Imran et al. investigated chemistry problems in order to create mathematical representations of various chemical sub- stances, with each compound having its own representation (see [10]). Navigation can be understood within a graphical structure in which the point robot or navigating agent moves from vertex to vertex of a graph. e robot can find its location by finding the distance from a fixed set of vertices also called landmarks. ere is no idea of direction and visibility in a graph, but the point robot can find the dis- tances from a fixed set of landmarks (see [11]). Melter and Tomescu worked on the metric distances used in image processing, for example, chessboard distance and the city block distance, and they also studied the applications to pattern recognition problems (see [12]). Raza investigated the chemistry application of polyphenyl and spiro chains (see [13]). Caceres et al. described the metric dimensions of graphs in coin weighing and mastermind games (see [14]). Hindawi Journal of Mathematics Volume 2022, Article ID 6738129, 9 pages https://doi.org/10.1155/2022/6738129