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Start Over Creator Zhou, Bo

1. On the sum of powers of Laplacian eigenvalues of bipartite graphs

Creator:
Zhou, Bo and Ilić
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Laplacian eigenvalues, incidence energy, Kirchhoff index, and Laplacian Estrada index
Language:
English
Description:
For a bipartite graph $G$ and a non-zero real $\alpha $, we give bounds for the sum of the $\alpha $th powers of the Laplacian eigenvalues of $G$ using the sum of the squares of degrees, from which lower and upper bounds for the incidence energy, and lower bounds for the Kirchhoff index and the Laplacian Estrada index are deduced.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Ordering the non-starlike trees with large reverse Wiener indices

Creator:
Li, Shuxian and Zhou, Bo
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
distance, diameter, Wiener index, reverse Wiener index, trees, starlike trees;, and caterpillars
Language:
English
Description:
The reverse Wiener index of a connected graph $G$ is defined as \[ \Lambda (G)=\frac {1}{2}n(n-1)d-W(G), \] where $n$ is the number of vertices, $d$ is the diameter, and $W(G)$ is the Wiener index (the sum of distances between all unordered pairs of vertices) of $G$. We determine the $n$-vertex non-starlike trees with the first four largest reverse Wiener indices for $n\ge 8$, and the $n$-vertex non-starlike non-caterpillar trees with the first four largest reverse Wiener indices for $n\ge 10$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Remarks on spectral radius and Laplacian eigenvalues of a graph

Creator:
Zhou, Bo and Cho, Han Hyuk
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
spectral radius, Laplacian eigenvalue, and strongly regular graph
Language:
English
Description:
Let $G$ be a graph with $n$ vertices, $m$ edges and a vertex degree sequence $(d_1, d_2, \dots , d_n)$, where $d_1 \ge d_2 \ge \dots \ge d_n$. The spectral radius and the largest Laplacian eigenvalue are denoted by $\rho (G)$ and $\mu (G)$, respectively. We determine the graphs with \[ \rho (G) = \frac{d_n - 1}{2} + \sqrt{2m - nd_n + \frac{(d_n +1)^2}{4}} \] and the graphs with $d_n\ge 1$ and \[ \mu (G) = d_n + \frac{1}{2} + \sqrt {\sum _{i=1}^n d_i (d_i-d_n) + \Bigl (d_n - \frac{1}{2} \Bigr )^2}. \] We also present some sharp lower bounds for the Laplacian eigenvalues of a connected graph.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public