<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

Publié en ligne: 02 juin 2022

Pages: 133 - 160

Reçu: 13 juil. 2021

Accepté: 10 nov. 2021

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

Mots clés
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

Publié en ligne: 02 juin 2022

Pages: 133 - 160

Reçu: 13 juil. 2021

Accepté: 10 nov. 2021

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

Mots clésLaplacian 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.

Mots clés
Laplacian matrix, Laplacian integral graphs, Laplacian energy, First zagreb index, Second zagreb index