In this paper, we study the spectral radius of graphs of order
n with
κ(
G) ≤
k. We show that among those graphs, the maximal spectral radius is obtained uniquely at
Knk{K_{n}^{k}}, which is the graph obtained by joining
k edges from
k vertices of
K
n-1 to an isolated vertex. We also show that the spectral radius of
Knk{K_{n}^{k}} will be very close to
n − 2 for a fixed
k and a sufficiently large
n.
Keywords Energy levels - Spectral radius - Connectivity - Edge-connectivity