Given a finite group G, let X be the set of those primes which divide the order of G. A square root prime divisors graph of G is defined as a graph whose vertices are the elements of X with an edge between two elements if they are related by  where n is a natural number, p and q are two distinct primes in X, and α and β are non-negative integers. The aim of this paper is to study square root prime divisors graphs of a finite group.

finite groups, complete graph, planar graph, threshold graph, congruence class.

Received: February 27, 2022; Accepted: March 29, 2022; Published: May 23, 2022

How to cite this article: Howida Adel AlFran, The square root prime divisors graph of a finite group, JP Journal of Algebra, Number Theory and Applications 55 (2022), 53-71. http://dx.doi.org/10.17654/0972555522019

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] Zeinab Akhlaghi, Carlo Casolo, Silvio Dolfı, Emanuele Pacifıci and Lucia Sanus, On the character degree graph of finite groups. Annali di Matematica Pura ed Applicata (1923-), 198(5) (2019), 1595-1614.
[2] Doostabadi Alireza, Erfanian Ahmad and Jafarzadeh Abbas, Some results on the power graphs of finite groups, ScienceAsia 41 (2015), 73-78.
[3] Milica Andjeli’c and Slobodan K Simi’c, Some notes on the threshold graphs, Discrete Mathematics 310(17-18) (2010), 2241-2248.
[4] Sudip Bera and A. K. Bhuniya, On enhanced power graphs of finite groups, Journal of Algebra and its Applications 17(08) (2018), 1850146.
[5] Peter J. Cameron, Pallabi Manna and Ranjit Mehatari, On finite groups whose power graph is a cograph, Journal of Algebra 2022.
[6] Miroslav Fiedler, Eigenvalues of nonnegative symmetric matrices, Linear Algebra and its Applications 9 (1974), 119-142.
[7] L.-K. Hua, Introduction to Number Theory, Springer Science and Business Media, 2012.
[8] Mark L. Lewis, An overview of graphs associated with character degrees and conjugacy class sizes in finite groups, The Rocky Mountain Journal of Mathematics 38(1) (2008), 175-211.
[9] Manjeet Saini, Sanhan Muhammad Salih Khasraw, Amit Sehgal and Dalip Singh, On co-prime order graphs of finite abelian p-groups, J. Math. Comput. Sci. 11(6) (2021), 7052-7061.
[10] Colin L. Starr and Galen E. Turner, Planar groups, Journal of Algebraic Combinatorics 19(3) (2004), 283-295.