On the zero forcing number and propagation time of oriented graphs

Hayat, Sakander; Siddiqui, Hafız Muhammad Afzal; Imran, Muhammad; Ikhlaq, Hafiz Muhammad; Cao, Jinde

doi:10.3934/math.2021111

Cited by 4 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similar studies on analyzing derivatives of path graphs and cycle graphs have been discussed in the literature before. The article [20] by Hayat et al discusses a zero forcing number and the propagation of oriented versions of graphs derived from path graphs and cycle graphs. We aimed at identifying what factors other than ∆ influence the value of χ s for inflating graphs which are derivatives of path graphs, cycle graphs and star graphs.…”

Section: Novelty Of the Articlementioning

confidence: 99%

An Analysis of the Factors Influencing the Strong Chromatic Index of Graphs Derived by Inflating a Few Common Classes of Graphs

Vikram

Balaji

2023

Symmetry

View full text Add to dashboard Cite

The problem of strong edge coloring discusses assigning colors to the edges of a graph such that distinct colors are assigned to any two edges which are either adjacent to each other or are adjacent to a common edge. The least number of colors required to define a strong edge coloring of a graph is called its strong chromatic index. This problem is equivalent to the problem of assigning collision-free frequencies to the links between the elements of a wireless sensor network. In this article, we discuss a novel way of generating new graphs from existing graphs. This graph construction is known as inflating a graph. We discuss the strong chromatic index of graphs generated by inflating some common classes of graphs and graphs derived from them. In particular, we consider the cycle graph, which is symmetric in nature, and graphs such as the path graph and the star graph, which are not symmetric. Further, we analyze the factors which influence the strong chromatic index of these inflated graphs.

show abstract

Section: Novelty Of the Articlementioning

confidence: 99%

An Analysis of the Factors Influencing the Strong Chromatic Index of Graphs Derived by Inflating a Few Common Classes of Graphs

Vikram

Balaji

2023

Symmetry

View full text Add to dashboard Cite

show abstract

“…In order to have an unimpeded interconnection network, we must think about the fault tolerance of a graph. There are many references focused on the fault tolerance of interconnection networks (see, for example [3][4][5][6][7][8][9][10]).…”

Section: Introductionmentioning

confidence: 99%

The m-Component Connectivity of Leaf-Sort Graphs

Wang,

Li,

Zhao

2024

Mathematics

View full text Add to dashboard Cite

Connectivity plays an important role in measuring the fault tolerance of interconnection networks. As a special class of connectivity, m-component connectivity is a natural generalization of the traditional connectivity of graphs defined in terms of the minimum vertex cut. Moreover, it is a more advanced metric to assess the fault tolerance of a graph G. Let G=(V(G),E(G)) be a non-complete graph. A subset F(F⊆V(G)) is called an m-component cut of G, if G−F is disconnected and has at least m components (m≥2). The m-component connectivity of G, denoted by cκm(G), is the cardinality of the minimum m-component cut. Let CFn denote the n-dimensional leaf-sort graph. Since many structures do not exist in leaf-sort graphs, many of their properties have not been studied. In this paper, we show that cκ3(CFn)=3n−6 (n is odd) and cκ3(CFn)=3n−7 (n is even) for n≥3; cκ4(CFn)=9n−212 (n is odd) and cκ4(CFn)=9n−242 (n is even) for n≥4.

show abstract

Exploring the Significance and Paradoxical Nature of the Zero Value in Mathematics Using Artificial Intelligence

et al. 2023

2023 4th International Conference on Smart Electronics and Communication (ICOSEC)

View full text Add to dashboard Cite

On the zero forcing number and propagation time of oriented graphs

Cited by 4 publications

References 13 publications

An Analysis of the Factors Influencing the Strong Chromatic Index of Graphs Derived by Inflating a Few Common Classes of Graphs

An Analysis of the Factors Influencing the Strong Chromatic Index of Graphs Derived by Inflating a Few Common Classes of Graphs

The m-Component Connectivity of Leaf-Sort Graphs

Exploring the Significance and Paradoxical Nature of the Zero Value in Mathematics Using Artificial Intelligence

Contact Info

Product

Resources

About