Special Issue "Discrete and Fractional Mathematics: Symmetry and Applications"

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics and Symmetry".

Deadline for manuscript submissions: 30 June 2021.

Special Issue Editors

Prof. Dr. Jose M. Rodriguez
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Guest Editor
Department of Mathematics, Carlos III University of Madrid-Leganés Campus, Avenida de la Universidad 30, CP-28911, Leganés, Madrid, Spain
Interests: discrete mathematics; fractional calculus; topological indices; polynomials in graphs; geometric function theory; geometry; approximation theory
Special Issues and Collections in MDPI journals
Prof. Dr. José M. Sigarreta
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Guest Editor
Faculty of Mathematics. Autonomous University of Guerrero-Acapulco Campus, Calle Carlos E. Adame 54, Garita, CP-39650, Acapulco, Guerrero, Mexico
Interests: discrete mathematics; alliances in graphs; conformable and non-conformable calculus; geometry; topological indices
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Although discrete and fractional mathematics have played an important role in Mathematics, in recent years, this role has significantly increased in several branches of these fields, including but not limited to: topological indices, molecular descriptors, domination theory, differential of graphs, polynomials in graphs, alliances in graphs, Gromov hyperbolic graphs, complex systems, discrete geometry, fractional differential equations, fractional integral operators, and discrete and fractional inequalities.

The aim of this Special Issue is to attract leading researchers in these areas in order to include new high-quality results on these topics involving their symmetry properties, both from a theoretical and an applied point of view. 

Prof. Dr. Jose M. Rodriguez
Prof. Dr. José M. Sigarreta
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 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.

Keywords

  • Discrete mathematics
  • Graph theory
  • Topological indices
  • Molecular descriptors
  • Chemical graph theory
  • Mathematical chemistry
  • Graph optimization problems
  • Domination in graphs
  • Differential of graphs
  • Polynomials in graphs
  • Polynomials on topological indices
  • Alliances in graphs
  • Hyperbolic graphs
  • Complex systems
  • Discrete geometry
  • Fractional calculus
  • Fractional differential equations
  • Fractional integral operators
  • Conformable and non-conformable calculus
  • Discrete and fractional inequalities

Published Papers (1 paper)

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Research

Open AccessArticle
Icosahedral Polyhedra from D6 Lattice and Danzer’s ABCK Tiling
Symmetry 2020, 12(12), 1983; https://doi.org/10.3390/sym12121983 - 30 Nov 2020
Abstract
It is well known that the point group of the root lattice D6 admits the icosahedral group as a maximal subgroup. The generators of the icosahedral group H3 , its roots, and weights are determined in terms of those of D [...] Read more.
It is well known that the point group of the root lattice D6 admits the icosahedral group as a maximal subgroup. The generators of the icosahedral group H3 , its roots, and weights are determined in terms of those of D6 . Platonic and Archimedean solids possessing icosahedral symmetry have been obtained by projections of the sets of lattice vectors of D6 determined by a pair of integers (m1,m2) in most cases, either both even or both odd. Vertices of the Danzer’s ABCK tetrahedra are determined as the fundamental weights of H3 , and it is shown that the inflation of the tiles can be obtained as projections of the lattice vectors characterized by the pair of integers, which are linear combinations of the integers (m1,m2) with coefficients from the Fibonacci sequence. Tiling procedure both for the ABCK tetrahedral and the <ABCK> octahedral tilings in 3D space with icosahedral symmetry H3, and those related transformations in 6D space with D6 symmetry are specified by determining the rotations and translations in 3D and the corresponding group elements in D6. The tetrahedron K constitutes the fundamental region of the icosahedral group and generates the rhombic triacontahedron upon the group action. Properties of “K-polyhedron”, “B-polyhedron”, and “C-polyhedron” generated by the icosahedral group have been discussed. Full article
(This article belongs to the Special Issue Discrete and Fractional Mathematics: Symmetry and Applications)
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