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Advances in Discrete Applied Mathematics and Graph Theory, 3rd Edition
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Advances in Discrete Applied Mathematics and Graph Theory, 3rd Edition

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

Deadline for manuscript submissions: 31 March 2025 | Viewed by 2663

Special Issue Editors

Prof. Dr. Janez Žerovnik

E-Mail Website
Guest Editor
1. Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia
2. Institute of Mathematics, Physics, and Mechanics, 1000 Ljubljana, Slovenia
Interests: graph theory; discrete optimization; algorithms; heuristics and metaheuristics
Special Issues, Collections and Topics in MDPI journals
Dr. Darja Rupnik Poklukar

E-Mail Website
Guest Editor
Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia
Interests: graph theory; topological indices; stochastic processes
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since its origins in the 18th century, graph theory has been a branch of mathematics that is both motivated by and applied to real world problems. Research in discrete mathematics increased in the latter half of the twentieth century mainly due to development of digital computers. On the other side, the advances in technology of digital computers enables extensive application of new ideas from discrete mathematics to real-world problems.

This special issue intends to promote novel examples of application of graph theory and discrete mathematics, as well as purely theoretical works with foreseen impact to applications. The editors do not intend to narrow the scope of applications, and also encourage studies in standard areas of application that may be of particular interest at the time.

Contributions are welcome. The selection criteria will be based on the formal and technical soundness, and the relevance of the contribution.

Prof. Dr. Janez Žerovnik
Dr. Darja Rupnik Poklukar
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. 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

  • discrete optimization
  • graph algorithms
  • graph theory
  • applied mathematics and modeling
  • operations research

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Related Special Issue

Published Papers (2 papers)

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Research

18 pages, 681 KiB  
Article
On the Problems of CF-Connected Graphs for Kl,m,n
by Michal Staš and Mária Timková
Mathematics 2024, 12(13), 2068; https://doi.org/10.3390/math12132068 - 1 Jul 2024
Viewed by 580
Abstract
A connected graph, G, is Crossing Free-connected (CF-connected) if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G. We conjecture that a complete tripartite graph, [...] Read more.
A connected graph, G, is Crossing Free-connected (CF-connected) if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G. We conjecture that a complete tripartite graph, Kl,m,n, is CF-connected if and only if it does not contain any of the following as a subgraph: K1,2,7, K1,3,5, K1,4,4, K2,2,5, K3,3,3. We examine the idea that K1,2,7, K1,3,5, K1,4,4, and K2,2,5 are the first non-CF-connected complete tripartite graphs. The CF-connectedness of Kl,m,n with l,m,n≥3 is dependent on the knowledge of crossing numbers of K3,3,n. In this paper, we prove various results that support this conjecture. Full article
(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory, 3rd Edition)
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17 pages, 2999 KiB  
Article
On Unicyclic Graphs with Minimum Graovac–Ghorbani Index
by Snježana Majstorović Ergotić
Mathematics 2024, 12(3), 384; https://doi.org/10.3390/math12030384 - 24 Jan 2024
Viewed by 1538
Abstract
In discrete mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Chemical graph theory is concerned with non-trivial applications of graph theory to the solution of molecular problems. Its main goal is to [...] Read more.
In discrete mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. Chemical graph theory is concerned with non-trivial applications of graph theory to the solution of molecular problems. Its main goal is to use numerical invariants to reduce the topological structure of a molecule to a single number that characterizes its properties. Topological indices are numerical invariants associated with the chemical constitution, for the purpose of the correlation of chemical structures with various physical properties, chemical reactivity, or biological activity. They have found important application in predicting the behavior of chemical substances. The Graovac–Ghorbani (ABCGG) index is a topological descriptor that has improved predictive potential compared to analogous descriptors. It is used to model both the boiling point and melting point of molecules and is applied in the pharmaceutical industry. In the recent years, the number of publications on its mathematical properties has increased. The aim of this work is to partially solve an open problem, namely to find the structure of unicyclic graphs that minimize the ABCGG index. We characterize unicyclic graphs with even girth that minimize the ABCGG index, while we also present partial results for odd girths. As an auxiliary result, we compare the ABCGG indices of paths and cycles with an odd number of vertices. Full article
(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory, 3rd Edition)
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