The diameter of the non-nilpotent graph of a finite group

Document Type : Research Paper

Authors

Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Italy

Abstract

We prove that the graph obtained from the non-nilpotent graph of a finite group by deleting the isolated vertices is connected with diameter at most 3‎. ‎This bound is the best possible‎.

Keywords

Main Subjects


[1] A. Abdollahi and M. Zarrin, Non-nilpotent graph of a group, Comm. Algebra, 38 (2010) 4390–4403.
[2] I. M. Isaacs, Finite group theory, Graduate Studies in Mathematics, 92, American Mathematical Society, Provi-
dence, RI, 2008.
[3] R. Guralnick, B. Kunyavskiĭ, E. Plotkin and A. Shalev, Thompson-like characterizations of the solvable radical,
J. Algebra, 300 (2006) 363–375