The minimum Q-index of strongly connected bipartite digraphs with complete bipartite subdigraphs

Abstract

Let ${\mathcal{G}}_{n,p,q}$ denote the set of strongly connected bipartite digraphs on $n$ vertices which contain a complete bipartite subdigraph $\overleftrightarrow{K_{p,q}}$, where $p,q,n$ are positive integers and $p+q\le n$. In this paper, we study the Q-index (i.e. the signless Laplacian spectral radius) of ${\mathcal{G}}_{n,p,q}$, and determine the extremal digraph that has the minimum Q-index.

arXiv comment11 pages, 2 figures