Guihai Yu

The Signless Laplacian Spectral Radius of Unicyclic Graphs with Graph Constraints

In this paper, we study the signless Laplacian spectral radius of unicyclic graphs with prescribed number of pendant vertices or independence number. We also characterize the extremal graphs completely.

Signed graphs with small positive index of inertia

In this paper, the signed graphs with one positive eigenvalue are characterized, and the signed graphs with pendant vertices having exactly two positive eigenvalues are determined. As a consequence, the signed trees, the signed unicyclic graphs and the signed bicyclic graphs having one or two positive eigenvalues are characterized.

The number of spanning trees of a graph with given matching number

The number of spanning trees of a graph G is the total number of distinct spanning subgraphs of G that are trees. In this paper, we present sharp upper bounds for the number of spanning trees of a graph with given matching number.

The signless Laplacian spectral radius of graphs on surfaces

Let G be an n-vertex simple graph embeddable on a surface of Euler genus γ. We present the upper bounds for the signless Laplacian spectral radius of G in terms of n and γ, with further improvements when G is an outerplanar or Halin graph.

LAPLACIAN EIGENVALUES OF GRAPHS WITH GIVEN DOMINATION NUMBER

In this paper, we study the Laplacian eigenvalues of graphs on n vertices with domination number γ and present upper bounds for the Laplacian spectral radius and algebraic connectivity as well, which improve old results apparently.