Open Journal of Discrete Applied Mathematics (ODAM)

The aim of Open Journal of Discrete Applied Mathematics (ODAM) (2617-9687 Online, 2617-9679 Print) is to bring together research papers in different areas of algorithmic and applied mathematics as well as applications of mathematics in various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. To ensure fast publication, editorial decisions on acceptance or otherwise are taken within 4 to 12 weeks (three months) of receipt of the paper.

Accepted articles are immediately published online as soon as they are ready for publication. There is one volume containing three issues per year. The issues will be finalized in April, August, and December of every year. The printed version will be published in December of every year.

Latest Published Articles

Author(s): Johan Kok1
1Independent Mathematics Researcher, City of Tshwane, South Africa & Visiting Faculty at CHRIST (Deemed to be a University), Bangalore, India
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.

Author(s): Noha Mohammad Seyam1, Mohammed Ali Alghamdi2, Adnan Khalil3
1Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah Saudi Arabia.
2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
3Department Computer Sciences, Al-Razi Institute Saeed Park, Lahore Pakistan.
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 tpology. A key component of graph theory are graph invariants, which identify the structural characteristics of networks and graphs. Furthermore doescribed by graph invariants are computer, social, and internet networks.

Author(s): Saad Tobaili1, Haifa Ahmed2, Mohammed Alsharafi3
1Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla, Yemen.
2Department of Mathematics, Faculty of Education, Art and Science, Aden University, Aden, Yemen.
3Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, 34220 Esenler, Istanbul, Turkey.
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.

Author(s): Carlos A. Alfaro1, Christian Rubio-Montiel2, Adrián Vázquez Ávila3
1Banco de México, Ciudad de México, México
2División de Matemáticas e Ingeniería, FES Acatlán, Uiversidad Nacional Autónoma de México, Ciudad de México, México
3Subdirección de Ingeniería y Posgrado, Universidad Aeronáutica en Querétaro, Querétaro, México
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.

Author(s): Syed Ahtsham Ul Haq Bokhary1, Shehr Bano1
1Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
Abstract:

Let \(A\) and \(B\) be two graph and \(P(A,z)\) and \(P(B,z)\) are their chromatic polynomial, respectively. The two graphs \(A\) and \(B\) are said to be chromatic equivalent denoted by \( A \sim B \) if \(P(A,z)=P(B,z)\). A graph \(A\) is said to be chromatically unique(or simply \(\chi\)- unique) if for any graph \(B\) such that \(A\sim B \), we have \(A\cong B\), that is \(A\) is isomorphic to \(B\). In this paper, the chromatic uniqueness of a new family of \(6\)-bridge graph \(\theta(r,r,s,s,t,u)\) where \(2\leq r\leq s \leq t\leq u\) is investigated.

Author(s): Zhen Lin1
1School of Mathematics and Statistics, Qinghai Normal University, Xining, 810008, Qinghai, China
Abstract:

In mathematical chemistry, a large number of topological indices are used to predict the physicochemical properties of compounds, especially in the study of quantitative structure-proerty relationship (QSPR).
However, many topological indices have almost the same predictive ability. In this paper, we focus on how to use fewer topological indices to predict the physicochemical properties of compounds through the QSPR analysis of connectivity indices of benzene hydrocarbons.

Author(s): Emre Sevgi1, Gül Özkan Kizilirmak, Serife Büyükköse
1Department of Mathematics, Faculty of Science, Gazi University, Ankara, Turkey.
Abstract:

In this paper, we obtain the bounds for the Laplacian eigenvalues of a weighted graph using traces. Then, we find the bounds for the Kirchhoff and Laplacian Estrada indices of a weighted graph. Finally, we define the Laplacian energy of a weighted graph and get the upper bound for this energy.

Author(s): Phillip Mafuta1,2, Josiah Mushanyu3,2
1Department of Mathematics and Applied Mathematics IB74, University of the Free State, Bloemfontein, South Africa
2Department of Mathematics and Computational Sciences, University of Zimbabwe, Harare, Zimbabwe
3Department of Computing, Mathematical and Statistical Sciences, University of Namibia, Windhoek, Namibia
Abstract:

A number of results on claw-free, paw-free graphs have been presented in the literature. Although the proofs of such results are elegant, sound and valid, it has gone unnoticed that all the results about claw-free, paw-free graphs in the literature are a consequence of a result by Olariu [1]. The note, apart from covering the aforementioned gap, also provides an alternate proof to a result by Faudree and Gould found in [2] in that, an unnoticed consequence resulted in the characterization of claw-free, paw-free graphs.

Author(s): Rikio Ichishima1, Francesc-Antoni Muntaner-Batle2
1Department of Sport and Physical Education, Faculty of Physical Education, Kokushikan University, 7-3-1 Nagayama, Tama-shi, Tokyo 206-8515, Japan.
2Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of Newcastle, NSW 2308 Australia.
Abstract:

A graph \(G\) is said to be super edge-magic if there exists a bijective function \(f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left( G\right) \right\vert \right\}\) such that \(f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}\) and \(f\left(u\right) + f\left(v\right) + f\left(uv\right)\) is a constant for each \(uv\in E\left( G\right)\). In this paper, we study the super edge-magicness of graphs of order \(n\) with degree sequence \(s:4, 2, 2, \ldots, 2\). We also investigate the super edge-magic properties of certain families of graphs. This leads us to propose some open problems.

Author(s): Tricia Muldoon Brown1
1Department of Mathematical Sciences, Georgia Southern University, Savannah, GA, U.S.A.
Abstract:

Coronoids are nice chemical structures that may be represented mathematically in the planar hexagonal lattice. They have been well-studied both for their chemical properties and also their enumerative aspects. Typical approaches to the latter type of questions often include classification and algorithmic techniques. Here we study one simple class of coronoids called hollow hexagons. Notably, hollow hexagons may be represented with a collection of partitions on the set \(\{2,3,4,6\}\). The hollow hexagons are used to classify another family of primitive coronoids, which we introduce here, called lattice path coronoids. Techniques from lattice path enumeration are used to count these newly-defined structures within equivalence classes indexed by enclosing hollow hexagons.