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Symmetry
Special Issues
Symmetry in Graph and Hypergraph Theory II
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Symmetry in Graph and Hypergraph Theory II

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

Deadline for manuscript submissions: closed (31 July 2024) | Viewed by 2057

Special Issue Editors

Prof. Dr. Weifan Wang

E-Mail Website
Guest Editor
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Interests: graph coloring; graph labeling; graph partition; surviving rate; connectivity
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Min Chen

E-Mail Website
Guest Editor
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Interests: graph coloring; arboricity; forest partition; planar graph; graph embedding
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yongtang Shi

E-Mail Website
Guest Editor
Center for Combinatorics, Nankai University, Tianjin 300071, China
Interests: graph theory and its applications; combinatorial optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Graph and hypergraph theory is one of the most rapidly evolving fields of theoretical aspects of the study of discrete structures, and its applications are widely expanded in various areas, including computer science, artificial intelligence, data science, statistical physics, and chemistry. Symmetry is a basic attribute of aesthetic appreciation. A number of different symmetric measurements for networks and graphs have been developed and analyzed, becoming an important criterion that illustrates the structure and properties of graphs. The differences are due in part to the fact that symmetry can be interpreted in different ways, e.g., by means of knot theory or the automorphism group of a graph. Recently, symmetric measurements have been applied in many disciplines. Based on vertex orbits, it has long been used to define measures of the structural complexity of graphs and hypergraphs. Algebraic graph theory is a classical field where symmetry has been investigated extensively and the role of symmetry in network aesthetics attracts much more attention. In this Special Issue, we would like to invite you to submit your original research on the theory and applications of symmetry in graph and hypergraph theory.

Topics of interest include but are not limited to the following:

  • Graph and hypergraph;
  • Networks;
  • Coloring and labeling;
  • Partition and cover;
  • Ramsey theory;
  • Caylay graph and symmetric graph;
  • Extreme value problems;
  • Topological indices;
  • Graph algorithms;
  • Algebraic tools for graphs and hypergraphs.

Prof. Dr. Weifan Wang
Prof. Dr. Min Chen
Prof. Dr. Yongtang Shi
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 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.

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Published Papers (1 paper)

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Research

15 pages, 435 KiB  
Article
L(2, 1)-Labeling Halin Graphs with Maximum Degree Eight
by Haizhen Qiu, Yushi Che and Yiqiao Wang
Symmetry 2023, 15(1), 50; https://doi.org/10.3390/sym15010050 - 25 Dec 2022
Cited by 1 | Viewed by 1285
Abstract
Suppose that T is a plane tree without vertices of degree 2 and with at least one vertex of at least degree 3, and C is the cycle obtained by connecting the leaves of T in a cyclic order. Set [...] Read more.
Suppose that T is a plane tree without vertices of degree 2 and with at least one vertex of at least degree 3, and C is the cycle obtained by connecting the leaves of T in a cyclic order. Set G=T∪C, which is called a Halin graph. A k-L(2,1)-labeling of a graph G=(V,E) is a mapping f:V(G)→{0,1,…,k} such that, for any x1,x2∈V(G), it holds that |f(x1)−f(x2)|≥2 if x1x2∈E(G), and |f(x1)−f(x2)|≥1 if the distance between x1 and x2 is 2 in G. The L(2,1)-labeling number, denoted λ(G), of G is the least k for which G is k-L(2,1)-labelable. In this paper, we prove that every Halin graph G with Δ=8 has λ(G)≤10. This improves a known result, which states that every Halin graph G with Δ≥9 satisfies λ(G)≤Δ+2. This result, together with some known results, shows that every Halin graph G satisfies λ(G)≤Δ+6. Full article
(This article belongs to the Special Issue Symmetry in Graph and Hypergraph Theory II)
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