The distance spectral radius of digraphs

On spectral radius of strongly connected digraphs

 It is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. In this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.  

on spectral radius of strongly connected digraphs

it is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. in this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.

On the distance signless Laplacian spectral radius of graphs and digraphs

Let η(G) denote the distance signless Laplacian spectral radius of a connected graph G. In this paper, bounds for the distance signless Laplacian spectral radius of connected graphs are given, and the extremal graph with the minimal distance signless Laplacian spectral radius among the graphs with given vertex connectivity and minimum degree is determined. Furthermore, the digraph that minimize...

Improved Bounds for the Spectral Radius of Digraphs

Let G = (V,E) be a digraph with n vertices and m arcs without loops and multi-arcs. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. In this note, we obtain two sharp upper and lower bounds on ρ(G). These bounds improve those obtained by G.H. Xu and C.-Q Xu (Sharp bounds for the spectral radius of digraphs, Linear Algebra Appl. 430, 1607–1612, 2009).

Sharp bounds for the signless Laplacian spectral radius of digraphs