Laplacian energy and first Zagreb index of Laplacian integral graphs

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.

Keywords

• laplacian matrix
• laplacian integral graphs
• laplacian energy
• first zagreb index
• second zagreb index
• primary 05c50, 15a18
• secondary 05c76, 05c90