Huiqiu Lin

On the least distance eigenvalue and its applications on the distance spread

Let G be a connected graph with order n and D ( G ) be its distance matrix. Suppose that λ 1 ( D ) ? ? ? λ n ( D ) are the distance eigenvalues of G . In this paper, we give an upper bound on the least distance eigenvalue and characterize all the connected graphs with - 1 - 2 ? λ n ( D ) ? a where a is the smallest root of x 3 - x 2 - 11 x - 7 = 0 and a ? ( - 1 - 2 , - 2 ) . Furthermore, we show that connected graphs with λ n ( D ) ? - 1 - 2 are determined by their distance spectra. As applications, we give some lower bounds on the distance spread of graphs with given some parameters. In the end, we characterize connected graphs with the ( k + 1 ) th smallest distance spread.

Spectral radius of strongly connected digraphs

Let D be a digraph with vertex set V ( D ) and A be the adjacency matrix of D . The largest eigenvalue of A , denoted by ? ( D ) , is called the spectral radius of the digraph D . In this paper, we establish some sharp upper or lower bounds for digraphs with some given graph parameters, such as clique number, girth, and vertex connectivity, and characterize the corresponding extremal graphs. In addition, we give the exact value of the spectral radii of those digraphs.

The maximum Perron roots of digraphs with some given parameters

Abstract We characterize the extremal digraphs which attain the maximum Perron root of digraphs with given arc connectivity and number of vertices. We also characterize the extremal digraphs which attain the maximum Perron root of digraphs given diameter and number of vertices.

Remoteness and distance eigenvalues of a graph

Let

Colorings and spectral radius of digraphs

G

On the Aα-spectra of graphs

be a connected graph of order

Distance between distance spectra of graphs

n

Maximum size of digraphs with some parameters

with diameter

On the distance spectrum of graphs

d

Distance spectral radius of digraphs with given connectivity

. Remoteness