University of Isfahan Transactions on Combinatorics 2251-8657 9 2 2020 06 01 The diameter of the non-nilpotent graph of a finite group 111 114 24553 10.22108/toc.2020.122329.1719 EN Andrea Lucchini Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Italy Daniele Nemmi Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Italy Journal Article 2020 03 30 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. ‎‎Distance nilpotency hypercenter https://toc.ui.ac.ir/article_24553_dee375fdb4286c5043d4088be2199ae6.pdf