Computing edge version of metric and double metric dimensions of Kayak paddle graphs

Zahid

Rashid

et al. 2022

Journal of Chemistry

Self Cite

The field of graph theory is extensively used to investigate structure models in biology, computer programming, chemistry, and combinatorial optimization. In order to work with the chemical structure, chemists require a mathematical form of the compound. The chemical structure can be depicted using nodes (which represent the atom) and links (which represent the many types of bonds). As a result, a graph theoretic explanation of this problem is to give representations for the nodes of a graph such that different nodes have unique representations. This graph theoretic study is referred to as the metric dimension. In this article, we have computed the edge version of the metric dimension and doubly resolving sets for the family of cycle with chord C n t for n ≥ 6 and 2 ≤ t ≤ ⌊ n / 2 ⌋ .

Section: Definitionmentioning

confidence: 99%

Computing Edge Version of Resolvability and Double Resolvability of a Graph

Zahid

Rashid

et al. 2022

Journal of Chemistry

Self Cite

“…Chen et al [28] provided the first explicitly approximated lower and upper limits for the MDRSs problem. Ahmad et al studied the line graphs of n-Sunlet, prism [29], and kayak paddle graphs [30] for the MD and MDRSs, respectively. To find the smallest possible DRS, a variety of graph families have been examined, such as those involving prisms [31], convex polytopes [32], and Hamming graphs [33].…”

Section: Introductionmentioning

confidence: 99%

Double Metric Resolvability in Convex Polytopes

Alrowaili

Ali

et al. 2022

Journal of Mathematics

Self Cite

Nowadays, the study of source localization in complex networks is a critical issue. Localization of the source has been investigated using a variety of feasible models. To identify the source of a network’s diffusion, it is necessary to find a vertex from which the observed diffusion spreads. Detecting the source of a virus in a network is equivalent to finding the minimal doubly resolving set (MDRS) in a network. This paper calculates the doubly resolving sets (DRSs) for certain convex polytope structures to calculate their double metric dimension (DMD). It is concluded that the cardinality of MDRSs for these convex polytopes is finite and constant.

“…e authors in [33,34] demonstrated that the DMD of some convex polytope structures is finite and constant. e line graphs of chorded cycles [35], kayak paddle graphs [36], n-Sunlet, and prism graphs [37] were discovered to have the MD and DRSs. In [38], layersun graphs and associated line graphs were studied for the MDRSs.…”

Section: Introductionmentioning

confidence: 99%

Studies of Chordal Ring Networks via Double Metric Dimensions

Mathematical Problems in Engineering

Zahid

Javaid

et al. 2022

Locating the sources of information spreading in networks including tracking down the origins of epidemics, rumors in social networks, and online computer viruses, has a wide range of applications. In many situations, identifying where an epidemic started, or which node in a network served as the source, is crucial. But it can be difficult to determine the root of an outbreak, especially when data are scarce and noisy. The goal is to find the source of the infection by analysing data provided by only a limited number of observers, such as nodes that can indicate when and where they are infected. Our goal is to investigate where the least number of observers should be placed, which is similar to how to figure out the minimal doubly resolving sets in the network. In this paper, we calculate the double metric dimension of chordal ring networks C R n 1,3,5 by describing their minimal doubly resolving sets.