ODAM – Vol 7 – Issue 1 (2024) – PISRT https://old.pisrt.org Sat, 01 Jun 2024 04:35:03 +0000 en-US hourly 1 https://wordpress.org/?v=6.7 Calculating degree-based topological indices and m-polynomials for various interconnection networks https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-1-2024/calculating-degree-based-topological-indices-and-m-polynomials-for-various-interconnection-networks/ Tue, 27 Feb 2024 16:36:15 +0000 https://old.pisrt.org/?p=8285
ODAM-Vol. 7 (2024), Issue 1, pp. 21 - 38 Open Access Full-Text PDF
Noha Mohammad Seyam, Mohammed Ali Alghamdi and Adnan Khalil
Abstract: There are three different kinds of topological indices: spectrum-based, degree-based, and distance-based. We presented the \(K\)-swapped network for \(t\)-regular graphs in this study. We also computed various degree-based topological indices of the \(K\)-swapped network for \(t\)-regular graphs, eye, and \(n\)-dimensional twisted cube network. The metrics used to analyze the abstract structural characteristics of networks are called topological indices. We also calculate each of the aforementioned networks M-polynomials. A graph can be used to depict an interconnection network's structure. The processing nodes in the network are represented by vertices, while the links connecting the processor nodes are represented by edges. We can quickly determine the diameter and degree between the nodes based on the graph's topology. A key component of graph theory are graph invariants, which identify the structural characteristics of networks and graphs. Furthermore described by graph invariants are computer, social, and internet networks.]]>
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Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 1, pp. 21 – 38
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0096

Calculating Degree-Based Topological Indices and M-Polynomials for Various Interconnection Networks

Noha Mohammad Seyam\(^{1}\), Mohammed Ali Alghamdi\(^{2}\) and Adnan Khalil\(^{3,*}\)
\(^{1}\)Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah Saudi Arabia.; nmseyam@uqu.edu.sa; (N. M.S.)
\(^{2}\)Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.; Proff-malghamdi@hotmail.com; (M. A. A.)
\(^{3}\)Department Computer Sciences, Al-Razi Institute Saeed Park, Lahore Pakistan.; adnan8414626@gmail.com; (A. K.)

Copyright © 2024 Noha Mohammad Seyam, Mohammed Ali Alghamdi and Adnan Khalil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: December 16, 2023 – Accepted: January 24, 2024 – Published: February 27, 2024

Abstract

There are three different kinds of topological indices: spectrum-based, degree-based, and distance-based. We presented the \(K\)-swapped network for \(t\)-regular graphs in this study. We also computed various degree-based topological indices of the \(K\)-swapped network for \(t\)-regular graphs, eye, and \(n\)-dimensional twisted cube network. The metrics used to analyze the abstract structural characteristics of networks are called topological indices. We also calculate each of the aforementioned networks M-polynomials. A graph can be used to depict an interconnection network’s structure. The processing nodes in the network are represented by vertices, while the links connecting the processor nodes are represented by edges. We can quickly determine the diameter and degree between the nodes based on the graph’s topology. A key component of graph theory are graph invariants, which identify the structural characteristics of networks and graphs. Furthermore described by graph invariants are computer, social, and internet networks.

Keywords:

Interconnection networks, Topological indices, M-polynomials.
]]> Edge hub number of fuzzy graphs https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-1-2024/edge-hub-number-of-fuzzy-graphs/ Tue, 27 Feb 2024 16:32:54 +0000 https://old.pisrt.org/?p=8283
ODAM-Vol. 7 (2024), Issue 1, pp. 11 - 20 Open Access Full-Text PDF
Saad Tobaili, Haifa Ahmed and Mohammed Alsharafi
Abstract: Shadi I.K et al. [1] introduced the edge hub number of graphs. This work extends the concept to fuzzy graphs. We derive several properties of edge hub number of fuzzy graphs and establish some relations that connect the new parameter with other fuzzy graph parameters. Also, some bounds of such a parameter are investigated. Moreover, we provide empirical evidence examples to elucidate the behavior and implications of edge hub number of fuzzy graph parameters.]]>
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Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 1, pp. 11 – 20
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0095

Edge Hub Number of Fuzzy Graphs

Saad Tobaili\(^{1}\), Haifa Ahmed\(^{2}\) and Mohammed Alsharafi\(^{3,*}\)
\(^{1}\)Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla, Yemen.; saadaltobaili@yahoo.com
\(^{2}\)Department of Mathematics, Faculty of Education, Art and Science, Aden University, Aden, Yemen.; haifaahmed010@gmail.com
\(^{3}\)Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, 34220 Esenler, Istanbul, Turkey.; alsharafi205010@gmail.com

Copyright © 2024 Saad Tobaili, Haifa Ahmed and Mohammed Alsharafi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: October 1, 2023 – Accepted: January 10, 2024 – Published: February 27, 2024

Abstract

Shadi I.K et al. [1] introduced the edge hub number of graphs. This work extends the concept to fuzzy graphs. We derive several properties of edge hub number of fuzzy graphs and establish some relations that connect the new parameter with other fuzzy graph parameters. Also, some bounds of such a parameter are investigated. Moreover, we provide empirical evidence examples to elucidate the behavior and implications of edge hub number of fuzzy graph parameters.

Keywords:

Fuzzy graph, Hub number, Edge hub number
]]> Covering and 2-degree-packing numbers in graphs https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-1-2024/covering-and-2-degree-packing-numbers-in-graphs/ Tue, 27 Feb 2024 16:27:27 +0000 https://old.pisrt.org/?p=8281
ODAM-Vol. 7 (2024), Issue 1, pp. 1 - 10 Open Access Full-Text PDF
Carlos A. Alfaro, Christian Rubio-Montiel and Adrián Vázquez Ávila
Abstract: In this paper, we give a relationship between the covering number of a simple graph \(G\), \(\beta(G)\), and a new parameter associated to \(G\), which is called 2-degree-packing number of \(G\), \(\nu_2(G)\). We prove that \[\lceil \nu_{2}(G)/2\rceil\leq\beta(G)\leq\nu_2(G)-1,\] for any simple graph \(G\), with \(|E(G)|>\nu_2(G)\). Also, we give a characterization of connected graphs that attain the equalities.]]>
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Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 1, pp. 1 – 10
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0094

Covering and 2-degree-packing numbers in graphs

Carlos A. Alfaro\(^{1}\), Christian Rubio-Montiel\(^{2}\) and Adrián Vázquez Ávila\(^{3,*}\)
\(^{1}\)Banco de México, Ciudad de México, México; carlos.alfaro@banxico.org.mx
\(^{2}\)División de Matemáticas e Ingeniería, FES Acatlán, Uiversidad Nacional Autónoma de México, Ciudad de México,
México; christian.rubio@acatlan.unam.mx
\(^{3}\)Subdirección de Ingeniería y Posgrado, Universidad Aeronáutica en Querétaro, Querétaro, México;
adrian.vazquez@unaq.mx

Copyright © 2024 Carlos A. Alfaro, Christian Rubio-Montiel and Adrián Vázquez Ávila. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: September 29, 2023 – Accepted: December 12, 2024 – Published: February 27, 2024

Abstract

In this paper, we give a relationship between the covering number of a simple graph \(G\), \(\beta(G)\), and a new parameter associated to \(G\), which is called 2-degree-packing number of \(G\), \(\nu_2(G)\). We prove that \[\lceil \nu_{2}(G)/2\rceil\leq\beta(G)\leq\nu_2(G)-1,\] for any simple graph \(G\), with \(|E(G)|>\nu_2(G)\). Also, we give a characterization of connected graphs that attain the equalities.

Keywords:

2-degree-packing number, Vertex cover, Graph parameters.
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