On the bounds of Laplacian eigenvalues of k-connected graphs

Title:

On the bounds of Laplacian eigenvalues of k-connected graphs

Creator:

Chen, Xiaodan and Hou, Yaoping

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a19a0ffd-2ece-4f0b-9d0f-58bf5c7503e0
uuid:a19a0ffd-2ece-4f0b-9d0f-58bf5c7503e0
issn:0011-4642

Subject:

mathematics, k-connected graph, non-regular graph, algebraic connectivity, Laplacian spectral radius, maximum degree, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let µ_{n-1}(G) be the algebraic connectivity, and let µ_{1}(G) be the Laplacian spectral radius of a k-connected graph G with n vertices and m edges. In this paper, we prove that {\mu _{n - 1}}(G) \geqslant \frac{{2n{k^2}}}{{(n(n - 1) - 2m)(n + k - 2) + 2{k^2}}} , with equality if and only if G is the complete graph Kn or Kn − e. Moreover, if G is non-regular, then {\mu _1}(G) < 2\Delta - \frac{{2(n\Delta - 2m){k^2}}}{{2(n\Delta - 2m)({n^2} - 2n + 2k) + n{k^2}}} , where ▵ stands for the maximum degree of G. Remark that in some cases, these two inequalities improve some previously known results., Xiaodan Chen, Yaoping Hou., and Obsahuje seznam literatury

Language:

English

Rights:

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

Coverage:

701-712

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:3

Harvested from:

CDK

Metadata only:

false