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

摘要

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~n_k, 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)).