Radio Number for Generalized Petersen Graphs $P(n,2)$

Zhang, Feige; Nazeer, Saima; Habib, Mustafa; Zia, Tariq Javed; Ren, Zhendong

doi:10.1109/access.2019.2943835

Cited by 9 publications

(5 citation statements)

References 30 publications

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“…Authors [10] examined a comprehensive overview of graph labeling and the authors [11] discussed an assignment of radio numbers to triangular and rhombic honeycomb networks. In addition, the study of the radio and antipodal number for many different types of graphs has been the subject of intellectual research by several authors ( [12]; [13]; [14]; [15]; [16]; [17]; [18]; [19]; [20]; [21]; [22]).…”

Section: Related Workmentioning

confidence: 99%

Radio Labeling of Supersub—Division of Path Graphs

Mari,

Jeyaraj

2023

IEEE Access

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Motivated by the channel assignment problem, we study the radio labeling of graphs. The radio labeling problem is an important topic in discrete mathematics due to its diverse applications, e.g., frequency assignment in mobile communication systems, signal processing, circuit and sensor network design, etc. A graph labeling problem is an assignment of labels to the vertices or edges (or both) of a graph G that satisfy a mathematical constraint. Radio labeling, a vertex labeling of graphs with non-negative integers, finds an important application in the study of radio channel assignment problems. The maximum label used in a radio labeling is called its span, and the smallest possible span of a radio labeling is called the radio number of a graph. In this area, Liu and Zhu [1] provided important results by computing the exact values of rn(G) for paths and cycles when k is equal to the diameter for certain cases. In this paper, we determine the radio number rn(G) of G where G is the supersub−division of a path P n with n ≥ 3 vertices and a complete bipartite graph K 2,α with α ∈ N.

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Section: Related Workmentioning

confidence: 99%

Radio Labeling of Supersub—Division of Path Graphs

Mari,

Jeyaraj

2023

IEEE Access

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“…In research areas of sciences where networks constitute the basic and fundamental study blocks, graph theory (graph labeling, graph coloring etc.) is the most intuitive and fundamental approach to apply and study these sciences [1]- [4]. For example: (i) in computer sciences [5], data mining, database designing, image processing, network algorithms, resource allocation, clustering of web documents [6], phone networks(GSM phones) and bi-processor tasks.…”

Section: Introductionmentioning

confidence: 99%

The Edge Version of Metric Dimension for the Family of Circulant Graphs Cₙ(1, 2)

Nasir

et al. 2021

IEEE Access

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Graph theory is widely used to analyze the structure models in chemistry, biology, computer science, operations research and sociology. Molecular bonds, species movement between regions, development of computer algorithms, shortest spanning trees in weighted graphs, aircraft scheduling and exploration of diffusion mechanisms are some of these structure models. Let G = (V G , E G ) be a connected graph, where V G and E G represent the set of vertices and the set of edges respectively. The idea of the edge version of metric dimension is based on the distance of edges in a graph. Let R E G be the smallest set of edges in a connected graph G that forms a basis such that for every pair of edges e 1 , e 2 ∈ E G , there exists an edge e ∈ R E G for which d E G (e 1 , e) = d E G (e 2 , e) holds. In this paper, we show that the family of circulant graphs C n (1, 2) is the family of graphs with constant edge version of metric dimension.INDEX TERMS Line graph, Resolving sets, The edge version of metric dimension, Circulant graphs.

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“…In this paper, the numerical invariants concerning the total domination are studied for generalized Petersen graphs [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

The Numerical Invariants concerning the Total Domination for Generalized Petersen Graphs

Ting

Ali

Hameed

et al. 2020

Journal of Mathematics

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A subset S of V G is called a total dominating set of a graph G if every vertex in V G is adjacent to a vertex in S . The total domination number of a graph G denoted by γ t G is the minimum cardinality of a total dominating set in G . The maximum order of a partition of V G into total dominating sets of G is called the total domatic number of G and is denoted by d t G . Domination in graphs has applications to several fields. Domination arises in facility location problems, where the number of facilities (e.g., hospitals and fire stations) is fixed, and one attempts to minimize the distance that a person needs to travel to get to the closest facility. In this paper, the numerical invariants concerning the total domination are studied for generalized Petersen graphs.

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Radio Number for Generalized Petersen Graphs $P(n,2)$

Cited by 9 publications

References 30 publications

Radio Labeling of Supersub—Division of Path Graphs

Radio Labeling of Supersub—Division of Path Graphs

The Edge Version of Metric Dimension for the Family of Circulant Graphs Cₙ(1, 2)

The Numerical Invariants concerning the Total Domination for Generalized Petersen Graphs

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