Maximum Spectral Radius of Graphs with Connectivity at Most k and Minimum Degree at Least δ

Abstract

Li, Shiu, Chan and Chang [On the spectral radius of graphs with connectivity at most k, J. Math. Chem., 46 (2009), 340-346] studied the spectral radius of graphs of order n with κ(G) ≤ k and showed that among those graphs, the maximum spectral radius is obtained uniquely at \(K_k^n\), which is the graph obtained by joining k edges from k vertices of K n − 1 to an isolated vertex. In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k and minimum degree δ(G) ≥ k . We show that among those graphs, the maximum spectral radius is obtained uniquely at K k + (K δ − k + 1 ∪ K n − δ − 1).Keywordsconnectivityspectral radius