一类代数图的Cayley性
Cayley Properties of a Class of Algebraic Graphs

作者: 杨富元 , 章 超 :贵州大学数学与统计学院 贵州 贵阳;

关键词: Cayley图Hamilton图广义二面体群Cayley Graph Hamiltonian Graph Generalized Dihedral Group

摘要: 设R是一个有限环。本文基于代数图论的基本事实,研究一类重要的图族的Cayley性质,构造了代数图BΓn(R; f2, ..., fn)的一个无限子族,其中每个图都是Cayley图,在此基础上进一步考虑这类代数图的最大圈。

Abstract: Let R be a finite ring. Based on the basic facts of algebraic graph theory, this paper studies the Cayley properties of an important family of graphs, and constructs an infinite subfamily of algebraic graphs BΓn(R; f2, ..., fn), in which each graph is Cayley graph. On this basis, the maximal cycle of this kind of algebraic graph is further considered.

文章引用: 杨富元 , 章 超 (2021) 一类代数图的Cayley性。 应用数学进展, 10, 3618-3622. doi: 10.12677/AAM.2021.1011382

参考文献

[1] Lazebnik, F. and Ustimenko, V.A. (1993) New Examples of Graphs without Small Cycles and of Large Size. European Journal of Combinatorics, 14, 445-460.
https://doi.org/10.1006/eujc.1993.1048

[2] Lazebnik, F. and Woldar, A.J. (2001) General Properties of Some Families of Graphs Defined by Systems of Equations. Journal of Graph Theory, 38, 65-86.
https://doi.org/10.1002/jgt.1024

[3] Lazebnik, F. and Viglione, R. (2002) An Infinite Series of Regular Edge-But Not Vertex-Transitive Graphs. Journal of Graph Theory, 41, 249-258.
https://doi.org/10.1002/jgt.10064

[4] Lazebnik, F., Sun, S. and Wang, Y. (2017) Some Families of Graphs, Hypergraphs and Di- graphs Defined by Systems of Equations: A Survey. Lecture Notes of Seminario Interdisci- plinare di Matematica, 14, 105-142.

[5] Klisowski, M. and Ustimenko, V. (2012) On the Comparison of Cryptographical Properties of Two Different Families of Graphs with Large Cycle Indicator. Mathematics in Computer Science, 6, 181-198.

[6] Morris, D.W. (2012) 2-Generated Cayley Digraphs on Nilpotent Groups Have Hamiltonian Paths. Contributions to Discrete Mathematics, 7, 41-47.
https://doi.org/10.11575/cdm.v7i1.62051

[7] Biggs, N. (1992) Algebraic Graph Theory. Cambridge University Press, New York.

[8] Bondy, J.A. and Murty, U.S.R. (1976) Graph Theory with Applications. Macmillan, London.

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