New Perspectives of Graph Theory and Combinatorics

Dear Colleagues,

Graph theory and combinatorics remain central to modern mathematics, offering a deep well of unsolved problems, rich structural theory, and surprising connections to fields as varied as computer science, statistical physics, and optimization. This Special Issue is dedicated to exploring new perspectives in these areas, particularly topics that have seen recent growth in theoretical depth and computational insight.

We especially encourage submissions in the following areas: domination theory, including total, connected, Roman, and semi-total variants, as well as zero forcing, positive semidefinite zero forcing, power domination, and their connections to linear algebra, propagation processes, and control theory; independence number and related extremal and probabilistic problems; degree sequence problems, including characterizations, realizability questions, and invariants such as the residue of a graph; automated approaches to conjecture generation, including algorithmic heuristics that mimic mathematical discovery; new bounds, characterizations, and structural insights in classical and modern graph parameters; and interdisciplinary work linking combinatorics with algebraic, geometric, or logical methods.

While this Special Issue focuses firmly on the mathematical foundations of graph theory and combinatorics, we also welcome contributions that incorporate computational tools or explore how algorithmic processes can guide intuition and discovery in pure mathematics.

We invite original research articles and well-crafted surveys offering insight into ongoing developments, open problems, or novel frameworks.

Dr. Randy R. Davila
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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.