Special Issue "Highly Symmetrical Graphs"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 15 June 2019

Special Issue Editor

Guest Editor
Prof. Haruo Hosoya

Ochanomizu University (Emeritus) Otsuka 2-1-1, Bunkyo-ku, Tokyo 112-8610, Japan
Website | E-Mail

Special Issue Information

Dear Colleagues,

In graph theory, “symmetric graphs” have been well-defined and studied quite thoroughly. However, in the field of mathematical chemistry there remains an immense uncultivated area where many “highly symmetrical graphs” are discussed arising from molecular skeletons, crystal structures, reaction networks, etc. both in geometrical and topological senses.

Characteristic polynomials and several counting polynomials reflect the symmetry of a given graph. Here, the term symmetry refers to not only the geometry of the mathematical object concerned, but also the different features that can be deduced from the distribution of the zeroes, or the solutions, of the characteristic polynomial.

Consider, for example, the spectrum of the truncated dodecahedron, or a soccer ball fullerene composed of 60 vertices with 12 pentagons and 20 hexagons, which contains a nonuplet whose degeneracy is much larger than six, the highest number of the rotational symmetry of the graph in geometrical sense. This anomaly can be explained by drawing this graph with the tenfold “topological symmetry”, similar to the Heawood and Coxeter graphs. Accordingly efficient factorization of the characteristic polynomial can be performed deductively, and discussion on the perfect matching becomes feasible.

Hosoya and Harary proposed various series of fence graphs, from which so many highly symmetrical graphs were shown to be derived. There Hamiltonian wheel graphs, parallelogram-shaped polyhex graphs, and the so-called “torus benzenoid graphs” are also involved.

There is a challenging problem of how to design highly symmetrical graphs with highly degenerate spectra inductively but not deductively. Matching, especially the perfect matching of these graphs also should be discussed. Isospectrality or cospectrality related to these graphs has not yet been studied.

This Special Issue aims to address these knowledge gaps. We welcome the submission of challenging papers and proposals dealing with highly symmetrical graphs.

Prof. Haruo Hosoya
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 papers will be 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 1400 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.


  • highly symmetrical graph
  • topological symmetry
  • graph spectrum
  • characteristic polynomial
  • topological index
  • Hamiltonian graph
  • isospectral graph
  • cospectral graph
  • fence graph
  • perfect matching

Published Papers

This special issue is now open for submission.
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