关于小阶数非交换群的简化幂图
On the Reduced Power Graphs of Non-Abelian Groups of Small Order
DOI: 10.12677/AAM.2020.911230, PDF,    国家科技经费支持
作者: 仪钰婷, 吴玥雯, 安佳薇：西安石油大学理学院，陕西 西安
关键词: 简化幂图；独立数；有限群；团数；彩虹连通数；Reduced Power Graph； Independence Number； Finite Group； Clique Number； Rainbow Connection Number
摘要: 给定一个有限群G，群G上的简化幂图是以G的所有元素为顶点集合的一个简单图，其中两个不同的顶点x和y相邻当且仅当⊂或⊂。本文将给出14阶以内的非交换群的简化幂图的结构。此外本文也求了这些群简化幂图的独立数、团数以及彩虹连通数。
Abstract: Given a finite group G, the reduced power graph of G is an undirected graph with vertex set G, and two distinct vertices x and y are adjacent if and only if ⊂ or⊂. This paper characterizes the structures of the reduced power graphs of non-abelian groups of order at most 14. Moreover, this paper also computes the independence number, clique number, and the rainbow connection number of these graphs.
文章引用：仪钰婷, 吴玥雯, 安佳薇. 关于小阶数非交换群的简化幂图[J]. 应用数学进展, 2020, 9(11): 1990-1995. https://doi.org/10.12677/AAM.2020.911230

参考文献

[1] Kelarev, A.V. and Quinn, S.J. (2000) A Combinatorial Property and Power Graphs of Groups. Contributions to General Algebra, 12, 229-235.
[2] Chakrabarty, I., Ghosh, S. and Sen, M.K. (2009) Undirected Power Graphs of Semigroups. Semigroup Forum, 78, 410-426. [Google Scholar] [CrossRef] 
[3] Abawajy, J., Kelarev, A.V. and Chowdhury, M. (2013) Power Graphs: A Survey. Electronic Journal of Graph Theory and Applications, 1, 125-147. [Google Scholar] [CrossRef] 
[4] Rajkumar, R. and Anitha, T. (2017) Reduced Power Graph of a Group. Electronic Notes in Discrete Mathematics, 63, 69-76. [Google Scholar] [CrossRef] 

为你推荐