Abstract
AbstractThe power graph P(G) of a finite group G is the undirected simple graph with vertex set G, where two elements are adjacent if one is a power of the other. In this paper, the matching numbers of power graphs of finite groups are investigated. We give upper and lower bounds, and conditions for the power graph of a group to possess a perfect matching. We give a formula for the matching number for any finite nilpotent group. In addition, using some elementary number theory, we show that the matching number of the enhanced power graph $$P_e(G)$$
P
e
(
G
)
of G (in which two elements are adjacent if both are powers of a common element) is equal to that of the power graph of G.
Funder
Council of Scientific and Industrial Research India
DST, Government of India
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics
Reference17 articles.
1. L. Babai and P. J. Cameron, Automorphisms and enumeration of switching classes of tournaments, Electronic J. Combinatorics 7(1) (2000), article #R38.
2. R. Brandl, Finite groups all of whose elements are of prime power order, Bolletino Unione Matematica Italiana (5) 18 A (1981), 491–493.
3. N. G. de Bruijn, Ca. van Ebbenhorst Tengbergen, and D. Kruyswijk, On the set of divisors of a number, Nieuw Arch. Wiskunde (2) 23 (1951), 191–193.
4. P. J. Cameron. The power graph of finite group II. Journal of Group Theory, 13(6):779–783, 2010.
5. P. J. Cameron and N. Maslova, Criterion of unrecognizability of a finite group by its Gruenberg–Kegel graph, J. Algebra, in press; https://doi.org/10.1016/j.jalgebra.2021.12.005
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献