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

The set <italic>Si,n</italic> = {0, 1, 2, …, <italic>i −</italic> 1, <italic>i</italic> + 1, …, <italic>n −</italic> 1, <italic>n</italic>}, 1 ⩽ <italic>i</italic> ⩽ <italic>n</italic>, is called Laplacian realizable if there exists a simple connected undirected graph whose Laplacian spectrum is <italic>Si,n</italic>. The existence of such graphs was established by S. Fallat et all. In the present paper, we find the Laplacian energy and first Zagreb index of graphs whose Laplacian spectrum is <italic>Si,n</italic>.
</abstract>

The set Si,n = {0, 1, 2, …, i − 1, i + 1, …, n − 1, n}, 1 ⩽ i ⩽ n, is called Laplacian realizable if there exists a simple connected undirected graph whose Laplacian spectrum is Si,n. The existence of such graphs was established by S. Fallat et all. In the present paper, we find the Laplacian energy and first Zagreb index of graphs whose Laplacian spectrum is Si,n.

Laplacian energy and first Zagreb index of Laplacian integral graphs

Shanghai Jiao Tong University and MOE-LSC

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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

{"article-title":"Laplacian energy and first Zagreb index of Laplacian integral graphs"}

The set Si,n = {0, 1, 2, …, i − 1, i + 1, …, n − 1, n}, 1 ⩽ i ⩽ n, is called Laplacian realizable if there exists a simple connected undirected graph whose...

Laplacian energy and first Zagreb index of Laplacian integral graphs

Pubblicato online: 02 giu 2022

Pagine: 133 - 160

Ricevuto: 13 lug 2021

Accettato: 10 nov 2021

DOI: https://doi.org/10.2478/auom-2022-0023

Parole chiave
Laplacian matrix, Laplacian integral graphs, Laplacian energy, First zagreb index, Second zagreb index

© 2022 Abdul Hameed et al., published by Sciendo

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

Laplacian energy and first Zagreb index of Laplacian integral graphs

Pubblicato online: 02 giu 2022

Pagine: 133 - 160

Ricevuto: 13 lug 2021

Accettato: 10 nov 2021

DOI: https://doi.org/10.2478/auom-2022-0023

Parole chiaveLaplacian matrix, Laplacian integral graphs, Laplacian energy, First zagreb index, Second zagreb index

© 2022 Abdul Hameed et al., published by Sciendo

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

Parole chiave
Laplacian matrix, Laplacian integral graphs, Laplacian energy, First zagreb index, Second zagreb index