Projet de fin d'étude : The total graph of a commutative ring

Etudiant : ELOUAKKASS ABDELJALAL

Filière : Master Mathématiques Pures (MMP)

Encadrant : Pr. CHOULLI HANAN

Annèe : 2022

Résumé : The title of this master's project is "the total graph of a commutative ring", which is introduced and studied by David Anderson and Ayman Badawi in an article published in 2008. Let R be a commutative ring and Z(R) its set of zero-divisors . The total graph of R is a graph denoted by T(Γ(R)) such that the set vertex is R and two distinct vertices are adjacent if and only if their sum is a zero-divisor. The study of T(Γ(R)) breaks naturally into two cases depending on whether or not Z(R) is an ideal of R. This notion is a common point between two fields in mathematics; commutative ring theory and graph theory. The main goal of this association is to translate the properties of graphs into algebraic properties and so, using the results and methods of algebra to deduce theorems about graphs.