Generalized Cayley graphs over polygroups

被引：7
|
作者：
Heidari, Dariush [1 ]
Amooshahi, Marzieh [2 ]
Davvaz, Bijan [3 ]
机构：
[1] Mahallat Inst Higher Educ, Fac Sci, Mahallat, Iran
[2] Islamic Azad Univ, Young Researcher & Elite Club, Khomein Branch, Khomein, Iran
[3] Yazd Univ, Dept Math, Yazd, Iran
来源：
COMMUNICATIONS IN ALGEBRA | 2019年 / 47卷 / 05期
关键词：
Caylay graph; GCP-graph; group; polygroup; simple graph; COMBINATORIAL ASPECTS;
D O I：
10.1080/00927872.2018.1530254
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Polygroups are a generalization of groups in which the composition of any two elements are a non-empty set. In this paper, first we recall the concept of polygroups and introduce a new construction for building a polygroup from a polygroup and a non-empty set. Then we study the concept of generalized Cayley graphs over polygroups, say GCP-graphs. Then we prove some properties of them in order to answer this question: which simple graphs are GCP-graphs? Finally, we prove that every simple graph of order at most five is a GCP-graph.
引用
收藏
页码：2209 / 2219
页数：11
相关论文
共 50 条
  • [31] Integral Cayley Graphs over Finite Groups
    Konstantinova, Elena, V
    Lytkina, Dania
    ALGEBRA COLLOQUIUM, 2020, 27 (01) : 131 - 136
  • [32] Algebraic Cayley graphs over finite fields
    Lu, M.
    Wan, D.
    Wang, L. -P.
    Zhang, X. -D.
    FINITE FIELDS AND THEIR APPLICATIONS, 2014, 28 : 43 - 56
  • [33] Integral Cayley graphs over dicyclic group
    Cheng, Tao
    Feng, Lihua
    Huang, Hualin
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 566 : 121 - 137
  • [34] Cayley graphs of groupoids and generalized fat-trees
    Bahman Khosravi
    Indian Journal of Pure and Applied Mathematics, 2023, 54 : 1125 - 1131
  • [35] On maximal cliques of Cayley graphs over fields
    Chi Hoi Yip
    Journal of Algebraic Combinatorics, 2022, 56 : 323 - 333
  • [36] Spectra of Generalized Cayley Graphs on Finite Abelian Groups
    Zhu, Xiaomin
    Yang, Xu
    Chen, Jing
    ALGEBRA COLLOQUIUM, 2023, 30 (01) : 97 - 110
  • [37] Generalized Cayley maps and Hamiltonian maps of complete graphs
    Abas, Marcel
    DISCRETE MATHEMATICS, 2012, 312 (06) : 1106 - 1116
  • [38] Hamilton paths in Cayley graphs on generalized dihedral groups
    Alspach, Brian
    Chen, C. C.
    Dean, Matthew
    ARS MATHEMATICA CONTEMPORANEA, 2010, 3 (01) : 29 - 47
  • [39] Isomorphisms and Automorphisms of Generalized Semi-Cayley Graphs
    Chen, Jing
    Yang, Xu
    Zhu, Xiaomin
    ALGEBRA COLLOQUIUM, 2019, 26 (02) : 321 - 328
  • [40] Cayley graphs of groupoids and generalized fat-trees
    Khosravi, Bahman
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023, 54 (04): : 1125 - 1131
12345