Bounds for the (Laplacian) spectral radius of graphs with parameter $\alpha $

Title:

Bounds for the (Laplacian) spectral radius of graphs with parameter $\alpha $

Creator:

Tian, Gui-Xian and Huang, Ting-Zhu

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:be75b612-0a4c-4ee7-83ff-e31d60e854ed
uuid:be75b612-0a4c-4ee7-83ff-e31d60e854ed

Subject:

graph, adjacency matrix, Laplacian matrix, spectral radius, and bound

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Let $G$ be a simple connected graph of order $n$ with degree sequence $(d_1,d_2,\ldots ,d_n)$. Denote $(^\alpha t)_i = \sum \nolimits _{j\colon i \sim j} {d_j^\alpha }$, $(^\alpha m)_i = {(^\alpha t)_i }/{d_i^\alpha }$ and $(^\alpha N)_i = \sum \nolimits _{j\colon i \sim j} {(^\alpha t)_j }$, where $\alpha $ is a real number. Denote by $\lambda _1(G)$ and $\mu _1(G)$ the spectral radius of the adjacency matrix and the Laplacian matrix of $G$, respectively. In this paper, we present some upper and lower bounds of $\lambda _1(G)$ and $\mu _1(G)$ in terms of $(^\alpha t)_i $, $(^\alpha m)_i $ and $(^\alpha N)_i $. Furthermore, we also characterize some extreme graphs which attain these upper bounds. These results theoretically improve and generalize some known results.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

567-580

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:2

Harvested from:

CDK

Metadata only:

false