The lollipop graph is determined by its spectrum

Romain Boulet (1) , Bertrand Jouve (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

An even (resp. odd) lollipop is the coalescence of a cycle of even (resp. odd) length and a path with pendant vertex as distinguished vertex. It is known that the odd lollipop is determined by its spectrum and the question is asked by W. Haemers, X. Liu and Y. Zhang for the even lollipop. We revisit the proof for odd lollipop, generalize it for even lollipop and therefore answer the question. Our proof is essentially based on a method of counting closed walks.

Mots clés: graph; graph theory; spectral graph theory; graph determined by its spectrum; graphs determined by their spectrum; unicyclic graphs; lollipop; closed walks; counting closed walks; spectrum; adjacency matrix

Domaines: Mathématiques générales [math.GM]

Romain Boulet, Bertrand Jouve. The lollipop graph is determined by its spectrum. 2008. ⟨hal-00247105⟩