ODAM – Vol 7 – Issue 2 (2024) – PISRT https://old.pisrt.org Thu, 11 Jul 2024 17:18:13 +0000 en-US hourly 1 https://wordpress.org/?v=6.7 On edge irregularity strength of some classes of Toeplitz graphs https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-2-2024/on-edge-irregularity-strength-of-some-classes-of-toeplitz-graphs/ Sun, 07 Jul 2024 11:50:16 +0000 https://old.pisrt.org/?p=8380
ODAM-Vol. 7 (2024), Issue 2, pp. 23 - 34 Open Access Full-Text PDF
Noha Mohammad Seyam, Muhammad Faisal Nadeem
Abstract:An edge irregular \(k\)-labeling of a graph \(G\) is a labeling of vertices of \(G\) with labels from the set \(\{1,2,3,\dots,k\}\) such that no two edges of \(G\) have same weight. The least value of \(k\) for which a graph \(G\) has an edge irregular \(k\)-labeling is called the edge irregularity strength of \(G\). Ahmad et. al. [1] showed the edge irregularity strength of some particular classes of Toeplitz graphs. In this paper we generalize those results and finds the exact values of the edge irregularity strength for some generalize classes of Toeplitz graphs. ]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 23-34
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0100

On edge irregularity strength of some classes of Toeplitz graphs

Noha Mohammad Seyam\(^1,\) Muhammad Faisal Nadeem$^{2,*}$
\(^1\) College of Applied Sciences Mathematical Sciences Department, Umm Al-Qura University, Makkah Saudi Arabia; nmseyam@uqu.edu.sa
\(^2\) Department of Mathematics, COMSATS University Islamabad Lahore Campus, Lahore 54000 Pakistan; mfaisalnadeem@ymail.com

Copyright © 2024 Noha Mohammad Seyam, Muhammad Faisal Nadeem. 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: May 14, 2024 – Accepted: June 09, 2024 – Published: June 30, 2024

Abstract

An edge irregular \(k\)-labeling of a graph \(G\) is a labeling of vertices of \(G\) with labels from the set \(\{1,2,3,\dots,k\}\) such that no two edges of \(G\) have same weight. The least value of \(k\) for which a graph \(G\) has an edge irregular \(k\)-labeling is called the edge irregularity strength of \(G\). Ahmad et. al. [1] showed the edge irregularity strength of some particular classes of Toeplitz graphs. In this paper we generalize those results and finds the exact values of the edge irregularity strength for some generalize classes of Toeplitz graphs.

Keywords:

irregular assignment; irregularity strength; edge irregularity strength; Toeplitz graph
]]> On the eccentric atom-bond sum-connectivity index https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-2-2024/on-the-eccentric-atom-bond-sum-connectivity-index/ Sun, 07 Jul 2024 11:47:47 +0000 https://old.pisrt.org/?p=8378
ODAM-Vol. 7 (2024), Issue 2, pp. 11 - 22 Open Access Full-Text PDF
Zaryab Hussain, Muhammad Ahsan Binyamin
Abstract:This note presents some upper bounds for the size of the upper deg-centric grapg \(G_{ud}\) of a simple connected graph G. Amongst others, a result for graphs for which a compliant graph \(G\) has \(G_{ud} \cong \overline G\) is presented. Finally, results for size minimality in respect upper deg-centrication and minimum size of such graph \(G\) are presented.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 11 – 22
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0099

On the eccentric atom-bond sum-connectivity index

Zaryab Hussain\(^{1,*}\), Muhammad Ahsan Binyamin\(^{2}\)
\(^{1}\) School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, Shaanxi 710129, China; zaryabhussain2139@gmail.com
\(^{2}\) Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan; ahsanbanyamin@gmail.com

Copyright © 2024 Zaryab Hussain, Muhammad Ahsan Binyamin. 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: June 9, 2024 – Accepted: June 29, 2024 – Published: June 30, 2024

Abstract

The eccentric atom-bond sum-connectivity \(\left(ABSC_{e}\right)\) index of a graph \(G\) is defined as \(ABSC_{e}(G)=\sum\limits_{uv\in E(G)}\sqrt{\frac{e_{u}+e_{v}-2}{e_{u}+e_{v}}}\), where \(e_{u}\) and \(e_{v}\) represent the eccentricities of \(u\) and \(v\) respectively. This work presents precise upper and lower bounds for the \(ABSC_{e}\) index of graphs based on their order, size, diameter, and radius. Moreover, we find the maximum and minimum \(ABSC_{e}\) index of trees based on the specified matching number and the number of pendent vertices.

Keywords:

eccentric atom-bond sum-connectivity index; tree; matching number; pendent vertex
]]> The inverse degree conditions for Hamiltonian and traceable graphs https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-2-2024/the-inverse-degree-conditions-for-hamiltonian-and-traceable-graphs/ Sun, 07 Jul 2024 11:45:11 +0000 https://old.pisrt.org/?p=8376
ODAM-Vol. 7 (2024), Issue 2, pp. 7 - 10 Open Access Full-Text PDF
Rao Li
Abstract:Let \(G = (V(G), E(G))\) be a graph with minimum degree at least \(1\). The inverse degree of \(G\), denoted \(Id(G)\), is defined as the sum of the reciprocals of degrees of all vertices in \(G\). In this note, we present inverse degree conditions for Hamiltonian and traceable graphs. ]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Discrete Applied Mathematics
Vol. 7 (2024), Issue 2, pp. 7 – 10
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0098

The inverse degree conditions for Hamiltonian and traceable graphs

Rao Li\(^{1,*}\)
\(^{1}\)Dept. of Computer Science, Engineering, and Math University of South Carolina Aiken, Aiken, SC 29801; raol@usca.edu

Copyright © 2024 Rao Li. 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: May 10, 2024 – Accepted: June 09, 2024 – Published: June 30, 2024

Abstract

Let \(G = (V(G), E(G))\) be a graph with minimum degree at least \(1\). The inverse degree of \(G\), denoted \(Id(G)\), is defined as the sum of the reciprocals of degrees of all vertices in \(G\). In this note, we present inverse degree conditions for Hamiltonian and traceable graphs.

Keywords:

the inverse degree; Hamiltonian graph, traceable graph.
]]> Note: Certain bounds in respect of upper deg-centric graphs https://old.pisrt.org/psr-press/journals/odam-vol-7-issue-2-2024/note-certain-bounds-in-respect-of-upper-deg-centric-graphs/ Sat, 01 Jun 2024 04:36:48 +0000 https://old.pisrt.org/?p=8334
ODAM-Vol. 7 (2024), Issue 2, pp. 1 - 6 Open Access Full-Text PDF
Johan Kok
Abstract:This note presents some upper bounds for the size of the upper deg-centric grapg \(G_{ud}\) of a simple connected graph G. Amongst others, a result for graphs for which a compliant graph \(G\) has \(G_{ud} \cong \overline G\) is presented. Finally, results for size minimality in respect upper deg-centrication and minimum size of such graph \(G\) are presented.]]>
INFORMATION MENU
Full-Text PDF

Open Journal of Discrete AppliedMathematics
Vol. 7 (2024), Issue 2, pp. 1 – 6
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2024.0097

Note: Certain bounds in respect of upper deg-centric graphs

Johan Kok\(^{1,*}\)
\(^{1}\)Independent Mathematics Researcher, City of Tshwane, South Africa & Visiting Faculty at CHRIST (Deemed to be a University), Bangalore, India; jacotype@gmail.com; johan.kok@christuniversity.in

Copyright © 2024 Johan Kok. 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: March 8, 2023 – Accepted: January 01, 2024 – Published: May 31, 2024

Abstract

This note presents some upper bounds for the size of the upper deg-centric grapg \(G_{ud}\) of a simple connected graph G. Amongst others, a result for graphs for which a compliant graph \(G\) has \(G_{ud} \cong \overline G\) is presented. Finally, results for size minimality in respect upper deg-centrication and minimum size of such graph \(G\) are presented.

Keywords:

Upper deg-centric graph; upper deg-centrication; equi-eccentric graph.
]]>