Topological Graph Theory and Discrete Geometry II
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".
Deadline for manuscript submissions: 30 April 2024 | Viewed by 1537
Special Issue Editor
Interests: topological graph theory; triangulations; discrete geometry
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Symmetry is one of the most basic and important notions in all fields of science, technology, and art. The notion of symmetry can be traced down through the entire history of human creative endeavors. The scope of this Special Issue encompasses common issues regarding combinatorial symmetries (automorphisms) of an abstract combinatorial structure and the geometric symmetries of geometric realizations of that structure.
For instance, a two-dimensional polyhedron can be regarded as a geometric realization of the corresponding topological graph embedding. A “combinatorial symmetry”, aka “automorphism”, of the topological embedding is defined as a permutation of the vertices that maps edges to edges and faces to faces. Combinatorial symmetry may be realized (but not necessarily) by some geometric symmetry of the original polyhedron; otherwise, the combinatorial symmetry is called a hidden symmetry of the polyhedron. Is the absence of hidden symmetries a sign of perfection of the polyhedron? Well, the five Platonic polyhedra have no hidden symmetries. Furthermore, although the regular triangulation of a torus with eight vertices cannot be realized in three-space as a regular polyhedron, it can be realized as such in four-space (the Lawrencenko polyhedron).
We invite contributions (research and review articles) covering a broad range of topics regarding combinatorial and geometric symmetries, including (but not limited to) the following:
- The interplay between combinatorial symmetries (automorphisms) of a combinatorial object and geometric symmetries of geometric realizations of the object;
- Topological graph theory; topological graph embeddings; combinatorial symmetries/automorphisms of embeddings; graph and map colorings; extremal graph theory; algorithms and optimization; flexibility of graph embeddings; triangulations and quadrangulations of surfaces and three-manifolds;
- Discrete geometry; symmetry groups; geometric polyhedra; mirror and rotational symmetries; chiral and axial symmetries; molecular symmetries;
- Any other relevant topics.
Dr. Serge Lawrencenko
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. Symmetry 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.
