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Axioms
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Advances in Discrete Mathematics and Theoretical Computer Science
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Advances in Discrete Mathematics and Theoretical Computer Science

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (20 December 2023) | Viewed by 2262

Special Issue Editors

Dr. Ching-Lueh Chang

E-Mail Website
Guest Editor
Department of Computer Science and Engineering, Yuan Ze University, Taoyuan 320315, Taiwan
Interests: discrete mathematics; sublinear algorithms; graph processes
Dr. Vadim Levit

E-Mail Website
Guest Editor
Department of Computer Science and Mathematics, Ariel University, Ariel 40700, Israel
Interests: combinatorial and algorithmic mathematics: graph theory, combinatorial optimization, and data analysis

Special Issue Information

Dear Colleagues,

We invite the submission of interesting and original results in discrete mathematics and theoretical computer science. Practical applications, experiments, and relationships with other disciplines are fine but not required. Papers submitted to this Special Issue should have one or several theorems as their main result. Furthermore, complete and correct proofs are necessary. In rare cases, rigorous mathematical proofs can be computer-assisted. However, in general, experimental results, including simulations and implementations of systems, should not be the focal point of any paper submitted to this Special Issue. Often, proofs of theorems are easy after one makes a smart observation, and such results are especially welcome in this Special Issue. We highly value natural mathematical problems such as those that can be described with very few words and that focus on the most fundamental mathematical objects, including graphs, strings, metric spaces, groups, etc.

Dr. Ching-Lueh Chang
Dr. Vadim Levit
Guest Editors

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. Axioms is an international peer-reviewed open access monthly 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 2400 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
  • exact algorithms
  • approximation algorithms
  • randomized algorithms
  • online algorithms
  • computability theory
  • computational complexity theory
  • computational logic
  • discrete mathematics
  • theoretical computer science

Published Papers (2 papers)

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Research

13 pages, 288 KiB  
Article
Pre-Emptive-Weights Goal-Programming for a Multi-Attribute Decision-Making Problem with Positive Correlation among Finite Criteria
by Juin-Han Chen and Hui-Chin Tang
Axioms 2023, 12(1), 20; https://doi.org/10.3390/axioms12010020 - 25 Dec 2022
Viewed by 874
Abstract
This paper analyzes the various properties of the positively correlated weights related to the subset of finite criteria in a multi-attribute decision-making problem. Given a finite number of criteria, the exact constraints of the positively correlated weights related to the subset of criteria [...] Read more.
This paper analyzes the various properties of the positively correlated weights related to the subset of finite criteria in a multi-attribute decision-making problem. Given a finite number of criteria, the exact constraints of the positively correlated weights related to the subset of criteria are presented. Introducing the non-Archimedean number, the associated bounded polyhedral-set is shown. The number of the extreme points in the bounded polyhedral-set will increase as the number of criteria increase. Applying the proposed efficient extreme-point method, the pre-emptive-weights-goal-programming optimal solution is shown. These theoretical global-maximum values of the positively correlated weights related to the subset of finite criteria are useful for practical applications. Full article
(This article belongs to the Special Issue Advances in Discrete Mathematics and Theoretical Computer Science)
12 pages, 275 KiB  
Article
Neighborhood Versions of Geometric–Arithmetic and Atom Bond Connectivity Indices of Some Popular Graphs and Their Properties
by Muhammad Shafii Abubakar, Kazeem Olalekan Aremu and Maggie Aphane
Axioms 2022, 11(9), 487; https://doi.org/10.3390/axioms11090487 - 19 Sep 2022
Cited by 1 | Viewed by 1182
Abstract
In this article, we introduce the neighborhood versions of two classical topological indices, namely neighborhood geometric–arithmetic and neighborhood atom bond connectivity indices. We study the graph-theoretic properties of these new topological indices for some known graphs, e.g., complete graph Kn, regular [...] Read more.
In this article, we introduce the neighborhood versions of two classical topological indices, namely neighborhood geometric–arithmetic and neighborhood atom bond connectivity indices. We study the graph-theoretic properties of these new topological indices for some known graphs, e.g., complete graph Kn, regular graph Rn, cycle graph Cn, star graph Sn, pendant graph, and irregular graph and further establish their respective bounds. We note that the neighbourhood geometric–arithmetic index of Kn, Rn, Cn, and Sn is equal to the number of edges. The neighborhood atom bond connectivity index of an arbitrary simple graph G is strictly less than the number of edges. Our results contribute to the literature in this direction. Full article
(This article belongs to the Special Issue Advances in Discrete Mathematics and Theoretical Computer Science)
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