Présentation d'un travail de thèse en co-tutelle

par Mme Neda Moradi

mardi 13 janv. 2026, 14:00 → 15:00 Europe/Paris

S3 365 (Sciences 3)

In this work, we investigate a representation-theoretic framework for encoding the combinatorial structure of graphs into algebraic objects. To each finite graph Γ=(V,E,ε), we associate a finite-dimensional module over the group algebra Fp[E], where p is an odd prime. The construction is based on the incidence relation between vertices and edges and induces a natural family of group characters, which in turn define a linear representation of the edge group. By linear extension, this representation yields a canonical Fp[E] -module, called the Γ-module.
We show that this module is completely reducible and that its character provides a powerful invariant of the underlying graph. In particular, we prove that isomorphic graphs give rise to isomorphic modules and hence to identical characters. Conversely, under suitable conditions, the equality of characters implies the isomorphism of the associated modules and reflects the equivalence of the original graphs. Explicit examples are presented to illustrate the construction and its effectiveness. This approach establishes a concrete bridge between graph theory and the representation theory of finite abelian groups, offering new algebraic tools for studying graph isomorphism problems.