Ji-Ming Guo

On the minimal energy ordering of trees with perfect matchings

The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the adjacency matrix of the graph. Zhang and Li [F. Zhang, H. Li, On acyclic conjugated molecules with minimal energies, Discrete Appl. Math. 92 (1999) 71-84] determined the first two smallest-energy trees of a fixed size with a perfect matching and showed that the third minimal energy is between two trees. This paper characterizes trees of a fixed size with a perfect matching with third minimal, fourth minimal and fifth minimal energies for n>=86 and third minimal, fourth minimal energies for 14@?n@?84.

An edge-separating theorem on the second smallest normalized Laplacian eigenvalue of a graph and its applications

Abstract Let λ 2 ( G ) be the second smallest normalized Laplacian eigenvalue of a graph G . In this paper, we investigate the behavior on λ 2 ( G ) when the graph G is perturbed by separating an edge. This result can be used to determine all trees and unicyclic graphs with λ 2 ( G ) ≥ 1 − 2 2 . Moreover, the trees and unicyclic graphs with λ 2 ( G ) = 1 − 2 2 are also determined, respectively.

The Normalized Laplacian Estrada Index of a Graph

In this paper, we define and investigate the normalized Laplacian Estrada index of a graph. Some bounds for the normalized Laplacian Estrada index of a graph in term of its vertex number, maximum (or minimum) degree are obtained, some inequalities between the normalized Laplacian Estrada and the normalized Laplacian energy are also obtained.

Bounds on normalized Laplacian eigenvalues of graphs

Let G be a simple connected graph of order n, where n≥2. Its normalized Laplacian eigenvalues are 0=λ1≤λ2≤⋯≤λn≤2. In this paper, some new upper and lower bounds on λn are obtained, respectively. Moreover, connected graphs with λ2=1 (or λn−1=1) are also characterized.MSC:05C50, 15A48.

The Smallest Spectral Radius of Graphs with a Given Clique Number

The first four smallest values of the spectral radius among all connected graphs with maximum clique size ω ≥ 2 are obtained.

Effects on the normalized Laplacian spectral radius of non-bipartite graphs under perturbation and their applications

The normalized Laplacian eigenvalues of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As an example of the application, the smallest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order is determined.

THE MINIMUM ALGEBRAIC CONNECTIVITY OF CATERPILLAR UNICYCLIC GRAPHS

A caterpillar unicyclic graph is a unicyclic graph in which the removal of all pendant vertices makes it a cycle. In this paper, the unique caterpillar unicyclic graph with minimum algebraic connectivity among all caterpillar unicyclic graphs is determined.

Bounding the sum of powers of normalized Laplacian eigenvalues of a graph

Let G be a simple connected graph of order n. Its normalized Laplacian eigenvalues are λ1≥λ2≥⋯≥λn−1≥λn=0. In this paper, new bounds on Sβ*(G)=∑i=1n−1λiβ (β ≠ 0, 1) are derived.

On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings

The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.

Coefficients of the Characteristic Polynomial of the (Signless, Normalized) Laplacian of a Graph

In this paper, we give a combinatorial expression for the fifth coefficient of the (signless) Laplacian characteristic polynomial of a graph. The first five normalized Laplacian coefficients are also given.