Barycentric Subdivision of Cayley Graphs With Constant Edge Metric Dimension

Koam, Ali N. A.; Ahmad, Ali

doi:10.1109/access.2020.2990109

Cited by 29 publications

(14 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…After the first introductory article [10], many authors investigated this invariant. Some of the latest articles for the reader's convenience are as [11], [14], [15], [22], [23].…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

On Mixed Metric Dimension of Some Path Related Graphs

Raza

2020

IEEE Access

View full text Add to dashboard Cite

A vertex k ∈ V G determined two elements (vertices or edges) , m ∈ V G ∪ E G , if d G (k,) = d G (k, m). A set R m of vertices in a graph G is a mixed metric generator for G, if two distinct elements (vertices or edges) are determined by some vertex set of R m. The least number of elements in the vertex set of R m is known as mixed metric dimension, and denoted as dim m (G). In this paper, the mixed metric dimension of some path related graphs is obtained. Those path related graphs are P 2 n the square of a path, T (P n) total graph of a path, the middle graph of a path M (P n), and splitting graph of a path S(P n). We proved that these families of graphs have constant and unbounded mixed metric dimension, respectively. We further presented an improved result for the metric dimension of the splitting graph of a path S(P n). INDEX TERMS Mixed metric dimension, Metric dimension, Edge metric dimension, Path related graphs.

show abstract

“…After the first introductory article [10], many authors investigated this invariant. Some of the latest articles for the reader's convenience are as [11], [14], [15], [22], [23].…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

On Mixed Metric Dimension of Some Path Related Graphs

Raza

2020

IEEE Access

View full text Add to dashboard Cite

show abstract

“…The general class of convex polytopes are discussed in the articles [28,29]. Another general class of graph obtained from different operations of graphs, is studied in [30]. General idea of metric which is known as partition dimension is discussed in [31][32][33], it provides a sharp utmost cardinality of partition metric basis.…”

Section: Introductionmentioning

confidence: 99%

Metric-Based Resolvability of Quartz Structure

Singla¹,

Al‐Wesabi²,

Pathania³

et al. 2022

Computers, Materials &Amp; Continua

View full text Add to dashboard Cite

Silica has three major varieties of crystalline. Quartz is the main and abundant ingredient in the crust of our earth. While other varieties are formed by the heating of quartz. Silica quartz is a rich chemical structure containing enormous properties. Any chemical network or structure can be transformed into a graph, where atoms become vertices and the bonds are converted to edges, between vertices. This makes a complex network easy to visualize to work on it. There are many concepts to work on chemical structures in terms of graph theory but the resolvability parameters of a graph are quite advance and applicable topic. Resolvability parameters of a graph is a way to getting a graph into unique form, like each vertex or edge has a unique identification by means of some selected vertices, which depends on the distance of vertices and its pattern in a particular graph. We have dealt some resolvability parameters of SiO 2 quartz. We computed the resolving set for quartz structure and its variants, wherein we proved that all the variants of resolvability parameters of quartz structures are constant and do not depend on the order of the graph.

show abstract

“…Recently, the edge metric dimension becomes a very common topic in resolvability and a lot of families of graphs are studied. Koam and Ahmad [15] studied edge metric dimension of barycentric subdivision of Cayley graph. e convex polytope graph was discussed by Zhang and Gao in [16] and Ahsan et al in [17].…”

Section: Introductionmentioning

confidence: 99%

On the Edge Metric Dimension of Different Families of Möbius Networks

Deng

Nadeem

Azeem

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

For an ordered subset Q e of vertices in a simple connected graph G , a vertex x ∈ V distinguishes two edges e 1 , e 2 ∈ E , if d x , e 1 ≠ d x , e 2 . A subset Q e having minimum vertices is called an edge metric generator for G , if every two distinct edges of G are distinguished by some vertex of Q e . The minimum cardinality of an edge metric generator for G is called the edge metric dimension, and it is denoted by dim e G . In this paper, we study the edge resolvability parameter for different families of Möbius ladder networks and we find the exact edge metric dimension of triangular, square, and hexagonal Möbius ladder networks.

show abstract

Barycentric Subdivision of Cayley Graphs With Constant Edge Metric Dimension

Cited by 29 publications

References 17 publications

On Mixed Metric Dimension of Some Path Related Graphs

On Mixed Metric Dimension of Some Path Related Graphs

Metric-Based Resolvability of Quartz Structure

On the Edge Metric Dimension of Different Families of Möbius Networks

Contact Info

Product

Resources

About