Submission Deadline: 30 November 2022 (closed) View: 184
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
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