Title: Four families of polynomials in spectral graph theorySpeaker: Miguel Angel Fiol Mora Affiliation: Universitat Politècnica de Catalunya Zoom: Contact Soffia Arnadottir
In this talk we describe four families of polynomials related to the spectrum of a graph. First, some known main results involving such polynomials, such as the spectral excess theorem characterizing distance-regularity, are discussed. Second, some new results giving bounds for the $k$-independence number $\alpha_k$ of a graph are presented. In this context, we comment on some relationships between the inertia (Cvetkovi\`c) and ratio (Hoffman) bounds of $\alpha_k$.