<abstract xmlns="http://www.w3.org/1999/xhtml">

Let G be a connected graph with n vertices, m edges. The distance signless Laplacian matrix DQ(G) is defined as DQ(G) = Diag(Tr(G)) + D(G), where Diag(Tr(G)) is the diagonal matrix of vertex transmissions and D(G) is the distance matrix of G. The distance signless Laplacian eigenvalues of G are the eigenvalues of DQ(G) and are denoted by δ1Q(G), δ2Q(G), ..., δnQ(G). δ1Q is called the distance signless Laplacian spectral radius of DQ(G). In this paper, we obtain upper and lower bounds for SDQ (G) in terms of the Wiener index, the transmission degree and the order of the graph.
</abstract>

Let G be a connected graph with n vertices, m edges. The distance signless Laplacian matrix DQ(G) is defined as DQ(G) = Diag(Tr(G)) + D(G), where Diag(Tr(G)) is the diagonal matrix of vertex transmissions and D(G) is the distance matrix of G. The distance signless Laplacian eigenvalues of G are the eigenvalues of DQ(G) and are denoted by δ1Q(G), δ2Q(G), ..., δnQ(G). δ1Q is called the distance signless Laplacian spectral radius of DQ(G). In this paper, we obtain upper and lower bounds for SDQ (G) in terms of the Wiener index, the transmission degree and the order of the graph.

On the spread of the distance signless Laplacian matrix of a graph

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On the spread of the distance signless Laplacian matrix of a graph"}

Let G be a connected graph with n vertices, m edges. The distance signless Laplacian matrix DQ(G) is defined as DQ(G) = Diag(Tr(G)) + D(G), where Diag(Tr(G))...

On the spread of the distance signless Laplacian matrix of a graph

Published Online: Aug 08, 2023

Page range: 38 - 45

Received: Apr 19, 2023

DOI: https://doi.org/10.2478/ausi-2023-0004

Keywords
distance matrix, distance signless Laplacian matrix, distance signless Laplacian eigenvalues, spread, Wiener index, transmission degree

© 2023 S. Pirzada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the spread of the distance signless Laplacian matrix of a graph

Published Online: Aug 08, 2023

Page range: 38 - 45

Received: Apr 19, 2023

DOI: https://doi.org/10.2478/ausi-2023-0004

Keywordsdistance matrix, distance signless Laplacian matrix, distance signless Laplacian eigenvalues, spread, Wiener index, transmission degree

© 2023 S. Pirzada et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
distance matrix, distance signless Laplacian matrix, distance signless Laplacian eigenvalues, spread, Wiener index, transmission degree