On Unicyclic Graphs Spectra : New Results

Makhlouf Hadji (1) , Ming Chau (1)

1 IRT SystemX

Let G = (V, E) be a unicyclic simple undirected graph. In this paper, we investigate the spectra of a particular class of unicyclic graphs G(q, n1) where q is the size of the unique cycle. Each vertex of the unique cycle is attached to n1 vertices. We provide the " exact values " of the extremal eigenvalues of the adjacency matrix A and the Laplacian matrix L of G, in contrast to lower and upper bounds reported in the literature.

Mots clés: Circulant matrices; Laplacian eigenvalues; Algebraic Connectivity; Unicyclic graph

Domaines: Mathématique discrète [cs.DM]; Réseaux et télécommunications [cs.NI]; Analyse numérique [cs.NA]

Makhlouf Hadji, Ming Chau. On Unicyclic Graphs Spectra : New Results. DCABES 2016 (15th International Symposium on Distributed Computing and Applications to Business, Engineering and Science), Aug 2016, Paris, France. pp.586-593, ⟨10.1109/CSE-EUC-DCABES.2016.245⟩. ⟨hal-01427303⟩