Special Issues
Table of Content

# Resolvability Parameters and their Applications

Submission Deadline: 30 November 2022 (closed) View: 85

### Guest Editors

Prof. Ali Ahmad, Jazan University, Saudi Arabia
Prof. Muhammad Imran, United Arab Emirates University, United Arab Emirates
Dr. Shahid Zaman, University of Sialkot, Pakistan

### Summary

Resolvability parameters are actually metric-based resolving sets, it comprises both components vertex and edge metric of a graph or network. These resolving parameters are implemented in different fields of science, such as in computer networking, chemical graph theory to study the generalized classes of graphs. In a recent survey on the resolvability parameters, it is found that more than 3100 (according to Google scholar) research articles have been published. To make more interest on the topic of resolvability parameters, we took an implementation in the field of computer networking and elaborated in the following manner.

Localization of a network is a methodology to access the exact location or position of a vertex (or a node). A compelling prototype is determining the precise location of a vertex in a network. When a computer sends a printing instruction in a workplace, localization an assist to find the nearest printer, a malfunctioning node, a network intruder, damaged equipment, illegal or misuse connections, as well as the location of a roving robot. Localization of a network is a strenuous, exorbitant costly, tedious and laborious process. Multiple nodes or vertices are chosen in such a way manner that the location of the needed vertex can be determined by its distinct representation (we can say either labeling, orientation, or location), with the help of chosen nodes. We have to pick the smallest number of vertices possible to make this method efficient. The most important object in this procedure is the locating set also known as the metric basis (in pure theoretical form) is the set of chosen vertices. The cardinality of the smallest feasible set of picked vertices (also known as metric dimension) is called a metric-resolving set. The task of identifying a graph's locating number is a non-deterministic polynomial-time hard problem, and the algorithmic challenge is yet unknown.

Similar to the resolving set, there are some edge dependent parameters which are known as edge resolving set also known as Edge metric dimension. Sometimes, both components edge and vertex are considered to locate the object in a localization which is known as mixed-metric resolving set or mixed-metric dimension. All these parameters are also known as resolvability parameters of a graph or network.

There are many generalized classes of graphs, computer networks, and chemical structures that are yet to study in terms of all these resolvability parameters. Therefore, the purpose of this special issue is to get some literature on the topic of locating set and to study more applications. We welcome review articles, original research work on the study of different computer networks, computer structures, and generalized classes of graphs.

The topics of interest include, but are not limited to following:

Resolvability parameters

Graph algorithms and complexity theory

Number theory and computer security

Metric-based resolving set

Edge metric dimension

Mixed-metric dimension

Topological indices

Mathematical chemistry

Algebraic construction of extremal graph

Entropy of graphs

### Published Papers

• Open Access

ARTICLE

Degree-Based Entropy Descriptors of Graphenylene Using Topological Indices

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.1, pp. 939-964, 2023, DOI:10.32604/cmes.2023.027254
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract Graph theory plays a significant role in the applications of chemistry, pharmacy, communication, maps, and aeronautical fields. The molecules of chemical compounds are modelled as a graph to study the properties of the compounds. The geometric structure of the compound relates to a few physical properties such as boiling point, enthalpy, π-electron energy, molecular weight. The article aims to determine the practical application of graph theory by solving one of the interdisciplinary problems describing the structures of benzenoid hydrocarbons and graphenylene. The topological index is an invariant of a molecular graph associated with the chemical More >

• Open Access

ARTICLE

Metric Basis of Four-Dimensional Klein Bottle

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3011-3024, 2023, DOI:10.32604/cmes.2023.024764
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract The Metric of a graph plays an essential role in the arrangement of different dimensional structures and finding their basis in various terms. The metric dimension of a graph is the selection of the minimum possible number of vertices so that each vertex of the graph is distinctively defined by its vector of distances to the set of selected vertices. This set of selected vertices is known as the metric basis of a graph. In applied mathematics or computer science, the topic of metric basis is considered as locating number or locating set, and it… More >

• Open Access

ARTICLE

Some Topological Values of Supramolecular Chain of Different Complexes of N-Salicylidene-L-Valine

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1899-1916, 2023, DOI:10.32604/cmes.2023.025071
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract L-valine is a glycogen-type amino acid regarded among the necessary mammalian amino acids. This is an amino acid that is essential for protein synthesis. N-salicylidene-L-valine is gaining a lot of attention because of its unique structure and increased catalytic and cytotoxic activity. We explore the chain of supramolecular dialkyltin N-salicylidene-L-valine complexes 2, 3, and 4 to learn more about this structure and its features regarding topological indices. We computed the first and second Randić index, harmonic index, sum-connectivity index, atom-bond-connectivity index, geometric arithmetic index and reduced reciprocal Randić index of Supramolecular Chain of Different Complexes More >

• Open Access

ARTICLE

A Drone-Based Blood Donation Approach Using an Ant Colony Optimization Algorithm

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.2, pp. 1917-1930, 2023, DOI:10.32604/cmes.2023.024700
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract This article presents an optimized approach of mathematical techniques in the medical domain by manoeuvring the phenomenon of ant colony optimization algorithm (also known as ACO). A complete graph of blood banks and a path that covers all the blood banks without repeating any link is required by applying the Travelling Salesman Problem (often TSP). The wide use promises to accelerate and offers the opportunity to cultivate health care, particularly in remote or unmerited environments by shrinking lab testing reversal times, empowering just-in-time lifesaving medical supply. More >

• Open Access

ARTICLE

Metric Identification of Vertices in Polygonal Cacti

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 883-899, 2023, DOI:10.32604/cmes.2023.025162
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path (geodesic) between them. A vertex x of G performs the metric identification for a pair (u, v) of vertices in G if and only if the equality between the distances of u and v with x implies that u = v (That is, the distance between u and x is different from the distance between v and x). The minimum number of vertices performing the metric identification for every pair of vertices in G defines the metric dimension of G. In this More >

• Open Access

ARTICLE

Entropies of the Y-Junction Type Nanostructures

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2665-2679, 2023, DOI:10.32604/cmes.2023.023044
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract Recent research on nanostructures has demonstrated their importance and application in a variety of fields. Nanostructures are used directly or indirectly in drug delivery systems, medicine and pharmaceuticals, biological sensors, photodetectors, transistors, optical and electronic devices, and so on. The discovery of carbon nanotubes with Y-shaped junctions is motivated by the development of future advanced electronic devices. Because of their interaction with Y-junctions, electronic switches, amplifiers, and three-terminal transistors are of particular interest. Entropy is a concept that determines the uncertainty of a system or network. Entropy concepts are also used in biology, chemistry, and More >

• Open Access

ARTICLE

Bounds on Fractional-Based Metric Dimension of Petersen Networks

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2697-2713, 2023, DOI:10.32604/cmes.2023.023017
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract The problem of investigating the minimum set of landmarks consisting of auto-machines (Robots) in a connected network is studied with the concept of location number or metric dimension of this network. In this paper, we study the latest type of metric dimension called as local fractional metric dimension (LFMD) and find its upper bounds for generalized Petersen networks GP(n, 3), where n ≥ 7. For n ≥ 9. The limiting values of LFMD for GP(n, 3) are also obtained as 1 (bounded) if n approaches to infinity. More >

• Open Access

ARTICLE

Minimal Doubly Resolving Sets of Certain Families of Toeplitz Graph

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2681-2696, 2023, DOI:10.32604/cmes.2023.022819
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract The doubly resolving sets are a natural tool to identify where diffusion occurs in a complicated network. Many real-world phenomena, such as rumour spreading on social networks, the spread of infectious diseases, and the spread of the virus on the internet, may be modelled using information diffusion in networks. It is obviously impractical to monitor every node due to cost and overhead limits because there are too many nodes in the network, some of which may be unable or unwilling to send information about their state. As a result, the source localization problem is to… More >

• Open Access

ARTICLE

Topological Aspects of Dendrimers via Connection-Based Descriptors

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.2, pp. 1649-1667, 2023, DOI:10.32604/cmes.2022.022832
（This article belongs to the Special Issue: Resolvability Parameters and their Applications)
Abstract Topological indices (TIs) have been practiced for distinct wide-ranging physicochemical applications, especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers, nanotubes and neural networks with respect to their certain properties such as solubility, chemical stability and low cytotoxicity. Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core. A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches, including numerical graph invariants. Among topological descriptors, Zagreb connection indices (ZCIs) have much More >