The minimum signless Laplacian spectral radius of graphs with given independence number

Abstract

The independence number α ( G ) of G is defined as the maximum cardinality of a set of pairwise non-adjacent vertices which is called an independent set. In this paper, we characterize the graphs which have the minimum spectral radius among all the connected graphs of order n with independence number α ( G ) ∈ 1 , 2 , n 2 , n 2 + 1 , n - 2 , n - 3 .