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Mathematics
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Research and Applications of Discrete Mathematics
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Research and Applications of Discrete Mathematics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 May 2024 | Viewed by 6788

Special Issue Editors

Dr. Naveed Ahmed Azam

E-Mail Website
Guest Editor
Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-850, Japan
Interests: discrete mathematics; operations research; artificial intelligence; cryptography; combinatorial optimization
Special Issues, Collections and Topics in MDPI journals
Dr. Kazuya Haraguchi

E-Mail Website
Co-Guest Editor
Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-8503, Japan
Interests: algorithms; discrete optimization; enumeration; metaheuristics; scheduling; operations research
Dr. Liang Zhao

E-Mail Website
Co-Guest Editor
Graduate School of Advanced Integrated Studies in Human Survivability (Shishu-Kan), Kyoto University, Kyoto 606-8503, Japan
Interests: network algorithms and optimization; machine learning; deep learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Research in discrete mathematics in theoretical and application aspects has significantly increased in recent decades. The first aim of this Special Issue is to encourage new theoretical results in discrete mathematics, such as results related to graph theory, theoretical computer science, and combinatorial optimization. The second aim of this Special Issue is to foster an exchange among the scientific community by solving practical problems from applied fields such as bioinformatics, chemo-informatics, material informatics, machine learning, cryptography, and operations research using discrete mathematics.

Any topics related to discrete mathematics are within the scope of this Special Issue. 

Dr. Naveed Ahmed Azam
Dr. Kazuya Haraguchi
Dr. Liang Zhao
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • graph theory
  • linear programming
  • discrete optimization
  • combinatorial algorithms
  • cryptography
  • bioinformatics

Published Papers (5 papers)

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Research

13 pages, 345 KiB  
Article
Axioms and Divisor Methods for a Generalized Apportionment Problem with Relative Equality
by Wenruo Lyu and Liang Zhao
Mathematics 2023, 11(15), 3270; https://doi.org/10.3390/math11153270 - 25 Jul 2023
Viewed by 877
Abstract
The allocation of seats in a legislative body to groups based on their size is a crucial issue in legal and political studies. However, recent findings suggest that an optimal allocation of seats may not be proportional to the size of the groups. [...] Read more.
The allocation of seats in a legislative body to groups based on their size is a crucial issue in legal and political studies. However, recent findings suggest that an optimal allocation of seats may not be proportional to the size of the groups. For instance, the European Parliament (EP) utilizes a subproportional system known as degressive proportionality. Unfortunately, current apportionment methods for the EP lack a rigorous axiomatic analysis and fail to adequately address equality. Building upon recent research on equality in subproportional settings, this paper proposed a novel generalization of existing axioms and divisor methods for proportionality to encompass subproportionality with relative equality. Specifically, we consider a function f(p)=a+bpγ on the standard number of seats for a group of size p, where a, b and γ are given non-negative constants, and a is an integer. This theory is exemplified through an empirical study focused on the EP. Full article
(This article belongs to the Special Issue Research and Applications of Discrete Mathematics)
25 pages, 824 KiB  
Article
Tangled Cord of FTTM4
by Noorsufia Abd Shukor, Tahir Ahmad, Mujahid Abdullahi, Amidora Idris and Siti Rahmah Awang
Mathematics 2023, 11(12), 2613; https://doi.org/10.3390/math11122613 - 07 Jun 2023
Viewed by 1477
Abstract
Fuzzy Topological Topographic Mapping (FTTM) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM, denoted as FTTMn, is an extension of FTTM [...] Read more.
Fuzzy Topological Topographic Mapping (FTTM) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM, denoted as FTTMn, is an extension of FTTM that is arranged in a symmetrical form. The special characteristic of FTTM, namely the homeomorphisms between its components, allows the generation of new FTTM. Later, the FTTMn can also be viewed as a graph. Previously, a group of researchers defined an assembly graph and utilized it to model a DNA recombination process. Some researchers then used this to introduce the concept of tangled cords for assembly graphs. In this paper, the tangled cord for FTTM4 is used to calculate the Eulerian paths. Furthermore, it is utilized to determine the least upper bound of the Hamiltonian paths of its assembly graph. Hence, this study verifies the conjecture made by Burns et al. Full article
(This article belongs to the Special Issue Research and Applications of Discrete Mathematics)
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19 pages, 3615 KiB  
Article
Enumerating Discrete Resonant Rossby/Drift Wave Triads and Their Application in Information Security
by Umar Hayat, Ikram Ullah, Ghulam Murtaza, Naveed Ahmed Azam and Miguel D. Bustamante
Mathematics 2022, 10(23), 4395; https://doi.org/10.3390/math10234395 - 22 Nov 2022
Cited by 1 | Viewed by 824
Abstract
We propose a new parametrization of the resonant Rossby/drift wave triads to develop an algorithm to enumerate all resonant triads in a given grid of wavenumbers. To arrive at such a parametrization, we have employed tools from arithmetic/algebraic geometry to project resonant triads [...] Read more.
We propose a new parametrization of the resonant Rossby/drift wave triads to develop an algorithm to enumerate all resonant triads in a given grid of wavenumbers. To arrive at such a parametrization, we have employed tools from arithmetic/algebraic geometry to project resonant triads on a certain class of conics. Further, we extend the newly developed algorithm for the enumeration of quasi-resonant triads and experimentally show that the said algorithm is robust to design the network of quasi-resonances. From the experimental results, we observed that the new algorithm enumerates all triads in low computation time when compared with the existing methods. Finally, we apply this work to information security by constructing a total order on the enumerated resonant triads to design a substitution box (S-box) generator. Via extensive analyses over several indicators (nonlinearity, algebraic complexity, linear and differential approximation probabilities, strict avalanche criteria, and bit independence criterion) we show that the newly developed S-box outperforms the S-boxes constructed by most of the existing schemes. Full article
(This article belongs to the Special Issue Research and Applications of Discrete Mathematics)
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5 pages, 226 KiB  
Article
Peeling Sequences
by Adrian Dumitrescu
Mathematics 2022, 10(22), 4287; https://doi.org/10.3390/math10224287 - 16 Nov 2022
Cited by 1 | Viewed by 1116
Abstract
Given an n-element point set in the plane, in how many ways can it be peeled off until no point remains? Only one extreme point can be removed at a time. The answer obviously depends on the point set. If the points [...] Read more.
Given an n-element point set in the plane, in how many ways can it be peeled off until no point remains? Only one extreme point can be removed at a time. The answer obviously depends on the point set. If the points are in convex position, there are exactly n! ways, which is the maximum number of ways for n points. But what is the minimum number? Full article
(This article belongs to the Special Issue Research and Applications of Discrete Mathematics)
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12 pages, 309 KiB  
Article
About AutoGraphiX Conjecture on Domination Number and Remoteness of Graphs
by Lidan Pei
Mathematics 2022, 10(19), 3706; https://doi.org/10.3390/math10193706 - 10 Oct 2022
Viewed by 920
Abstract
A set D⊆V(G) is called a dominating set if N[v]∩D≠∅ for every vertex v in graph G. The domination number γ(G) is the minimum cardinality of a [...] Read more.
A set D⊆V(G) is called a dominating set if N[v]∩D≠∅ for every vertex v in graph G. The domination number γ(G) is the minimum cardinality of a dominating set of G. The proximity π(v) of a vertex v is the average distance from it to all other vertices in graph. The remoteness ρ(G) of a connected graph G is the maximum proximity of all the vertices in graph G. AutoGraphiX Conjecture A.565 gives the sharp upper bound on the difference between the domination number and remoteness. In this paper, we characterize the explicit graphs that attain the upper bound in the above conjecture, and prove the improved AutoGraphiX conjecture. Full article
(This article belongs to the Special Issue Research and Applications of Discrete Mathematics)
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