Some properties of the distance Laplacian eigenvalues of a graph

Title:

Some properties of the distance Laplacian eigenvalues of a graph

Creator:

Aouchiche, Mustapha and Hansen, Pierre

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:80586b4f-21b2-4169-8cf5-7d055d06c42d
uuid:80586b4f-21b2-4169-8cf5-7d055d06c42d

Subject:

distance matrix, Laplacian, characteristic polynomial;, and eigenvalue

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The distance Laplacian of a connected graph $G$ is defined by $\mathcal {L} = {\rm Diag(Tr)}- \mathcal {D}$, where $\mathcal {D}$ is the distance matrix of $G$, and ${\rm Diag(Tr)}$ is the diagonal matrix whose main entries are the vertex transmissions in $G$. The spectrum of $\mathcal {L}$ is called the distance Laplacian spectrum of $G$. In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties of the distance Laplacian spectrum that enable us to derive the distance Laplacian characteristic polynomials for several classes of graphs.

Language:

English

Rights:

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

Coverage:

751-761

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:3

Harvested from:

CDK

Metadata only:

false