## “Structure of Vertex Neighbourhoods of Solubility Graphs”

Mercoledi 11 Maggio 2022, ore 10:00 - Aula 1BC45 - Banafsheh Akbari (Sahand University of Technology, Tabriz)

Abstract

The solubility graph associated with a finite group $G$ is a simple graph whose vertices are the elements of $G$, and there is an edge between two distinct vertices if and only if they generate a soluble subgroup.

In this talk, we focus on the set of neighbours of a vertex $x$ which we call it the solubilizer of $x$ in $G$, $Sol_G(x)$, investigating both arithmetic and structural properties of this set.