Maximum spectral radius of graphs with given connectivity, minimum degree and independence number ?
In this paper we study three families of graphs, one is the graphs of order n  with connectivity ?(G)?k ? ( G ) ? k and minimum degree ?(G)?k ? ( G ) ? k . We show that among the graphs in this family, the maximum spectral radius is obtained uniquely at Kk+(K??k+1?Kn???1) K k + ( K ? ? k + 1 ? K n ? ? ? 1 ) . Another family of the graphs we study is the family of bipartite graphs with order n and connectivity k . We show that among the graphs in this family the maximum spectral radius is obtained at a graph modified from K?n/2?,n?1??n/2? K ? n / 2 ? , n ? 1 ? ? n / 2 ? . The third family of graphs we have studied is the family of graphs with order n, connectivity k and independence number r. We determine the graphs in this family that have the maximum spectral radius.
maximum spectral radius connectivity independence number