Groupe d’études et de recherche en analyse des décisions

# The Minimum Spectral Radius of Graphs with a Given Clique Number

## Dragan Stevanovic et Pierre Hansen

We show that among connected graphs with maximum clique size $\omega$, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph $PK_{n-\omega,\omega}$, which consists of a complete graph $K_{\omega$ to a vertex of which a path $P_{n-\omega}$ is attached. For any fixed $\omega$, a small interval to which the spectral radii of kites $PK_{m,\omega, m\geq 1$ belong is exhibited.

, 14 pages