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Mathematics
Special Issues
Graph Theory and Applications, 3rd Edition
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Graph Theory and Applications, 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 30 January 2026 | Viewed by 495

Special Issue Editor

Prof. Dr. Darren Narayan

E-Mail Website
Guest Editor
School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, USA
Interests: graph theory; combinatorics; social networks; functional connectivity of the brain; mathematical modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Following the resounding success of our first two volumes, we are delighted to announce the launch of a third volume of this Special Issue. Your enthusiastic participation and high-quality contributions have solidified this series as a vibrant platform for cutting-edge research at the intersection of graph theory and its diverse applications.

For this third volume, we continue to welcome innovative submissions that explore the following topics:

  • Theoretical advancements in graph theory with potential real-world implications,
  • Interdisciplinary applications in biology, computer science, complex/social networks, and engineering,
  • Emerging domains where graph-based methods offer novel solutions (e.g., AI, sustainability, or healthcare systems).

Whether your work presents foundational theories or demonstrates impactful applications, we invite you to join this thriving scholarly dialogue. Let us push the boundaries of graph theory’s transformative potential together.

We look forward to receiving your contributions!

Prof. Dr. Darren Narayan
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
  • biology
  • computer science
  • complex and social networks
  • engineering

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Published Papers (2 papers)

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Research

13 pages, 271 KiB  
Article
Modular H-Irregularity Strength of Graphs
by Martin Bača, Marcela Lascsáková and Andrea Semaničová-Feňovčíková
Mathematics 2025, 13(16), 2599; https://doi.org/10.3390/math13162599 - 14 Aug 2025
Viewed by 87
Abstract
Two new graph characteristics, the modular edge H-irregularity strength and the modular vertex H-irregularity strength, are introduced. Lower bounds on these graph characteristics are estimated, and their exact values are determined for certain families of graphs. This demonstrates the sharpness of [...] Read more.
Two new graph characteristics, the modular edge H-irregularity strength and the modular vertex H-irregularity strength, are introduced. Lower bounds on these graph characteristics are estimated, and their exact values are determined for certain families of graphs. This demonstrates the sharpness of the presented lower bounds. Full article
(This article belongs to the Special Issue Graph Theory and Applications, 3rd Edition)
9 pages, 1015 KiB  
Article
Extremal Values of Second Zagreb Index of Unicyclic Graphs Having Maximum Cycle Length: Two New Algorithms
by Hacer Ozden Ayna
Mathematics 2025, 13(15), 2475; https://doi.org/10.3390/math13152475 - 31 Jul 2025
Viewed by 208
Abstract
It is well-known that the necessary and sufficient condition for a connected graph to be unicyclic is that its omega invariant, a recently introduced graph invariant useful in combinatorial and topological calculations, is zero. This condition could be stated as the condition that [...] Read more.
It is well-known that the necessary and sufficient condition for a connected graph to be unicyclic is that its omega invariant, a recently introduced graph invariant useful in combinatorial and topological calculations, is zero. This condition could be stated as the condition that the order and the size of the graph are equal. Using a recent result saying that the length of the unique cycle could be any integer between 1 and n − a1 where a1 is the number of pendant vertices in the graph, two explicit labeling algorithms are provided that attain these extremal values of the first and second Zagreb indices by means of an application of the well-known rearrangement inequality. When the cycle has the maximum length, we obtain the situation where all the pendant vertices are adjacent to the support vertices, the neighbors of the pendant vertices, which are placed only on the unique cycle. This makes it easy to calculate the second Zagreb index, as the contribution of the pendant edges to such indices is fixed, implying that we can only calculate these indices for the edges on the cycle. Full article
(This article belongs to the Special Issue Graph Theory and Applications, 3rd Edition)
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