On Two-Sided Cayley Graphs of Semigroups and Groups

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Annals of Combinatorics Pub Date : 2022-11-06 DOI:10.1007/s00026-022-00618-y

Farshad Hassani Hajivand, Behnam Khosravi

引用次数: 1

Abstract

In this paper, first we introduce the notion of two-sided Cayley graph of a semigroup. Then, we investigate some fundamental properties of these graphs and we use our results to give partial answers to some problems raised by Iradmusa and Praeger about two-sided group graphs (two-sided Cayley graphs of groups). Specially, as a consequence of our results, we determine all undirected two-sided Cayley graphs of groups which are connected. Furthermore, by introducing the notion of color-preserving automorphisms of a two-sided Cayley graph of a semigroup (group) and calculating them under some assumptions, we determine the family of color-vertex transitive two-sided Cayley graphs of semigroups (groups).

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半群和群的双面Cayley图

本文首先引入了半群的双侧Cayley图的概念。然后，我们研究了这些图的一些基本性质，并用我们的结果给出了Iradmusa和Praeger提出的关于双侧群图（群的双侧Cayley图）的一些问题的部分答案。特别地，由于我们的结果，我们确定了所有连通群的无向双侧Cayley图。此外，通过引入半群（群）的双侧Cayley图的保色自同构的概念并在一些假设下计算它们，我们确定了半群（组）的色顶点传递双侧Cayle图族。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Combinatorics 数学-应用数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches