The minimum spectral radius of Kr+1-saturated graphs

Abstract For a graph H , a graph G is H -saturated if G does not contain H as a subgraph but for any e ∈ E ( G ¯ ) , G + e contains H . In this note, we prove a sharp lower bound for the number of paths and walks on length 2 in n -vertex K r + 1 -saturated graphs. We then use this bound to give a lower bound on the spectral radii of such graphs which is asymptotically tight for each fixed r and n → ∞ .