On the (Laplacian) Spectral Radius of Bipartite Graphs with Given Number of Blocks

Abstract

The (Laplacian) spectral radius of a graph is the maximum eigenvalue of its adjacency matrix (Laplacian matrix, respectively). Let $\mathcal{G}(n,k)$ be the set of bipartite graphs with $n$ vertices and $k$ blocks. This paper gives a complete characterization for the extremal graph with the maximum spectral radius (Laplacian spectral radius, respectively) in $\mathcal{G}(n,k)$.