The Bounds of Spectral Radius of Graphs with a Given Size of Independent Set

Abstract

Let \(n, k\) be integers and \(k < n\). Denote by \(\mathcal{G}_{n,k}\) and \(\mathcal{G}'_{n,k}\) the set of graphs of order \(n\) with \(k\) independent vertices and the set of graphs of order \(n\) with \(k\) independent edges, respectively. The bounds of the spectral radius of graphs in \(\mathcal{G}_{n,k}\) and \(\mathcal{G}'_{n,k}\) are obtained.