University of Isfahan International Journal of Group Theory 2251-7650 13 4 2023 09 25 Group nilpotency from a graph point of view 351 367 27840 10.22108/ijgt.2023.137059.1834 EN Valentina Grazian Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Milano, Italy Andrea Lucchini Dipartimento di Matematica, Università di Padova, Padova, Italy Carmine Monetta Dipartimento di Matematica, Università di Salerno, Salerno, Italy 0000-0002-5426-1260 Journal Article 2023 03 07 Let $\Gamma_G$ denote a graph associated with a group $G$. A compelling question about finite groups asks whether or not a finite group $H$ must be nilpotent provided $\Gamma_H$ is isomorphic to $\Gamma_G$ for a finite nilpotent group $G$. In the present work we analyze the problem for different graphs that one can associate with a finite group, both reporting on existing answers and contributing to new ones. https://ijgt.ui.ac.ir/article_27840_ef94323ac4d0a692b7349f5ebe1c7d11.pdf