On the Local Laplacian Energy of Graphs

초록

For a simple graph G with n vertices, m edges, and Laplacian eigenvalues µ1,...,µn, the Laplacian energy LE(G) is defined as LE(G) = Pnk=1 |µk−2mn|. In this paper, we derive an upper bound for the variation in Laplacian energy resulting from a removal of a vertex and characterize the graphs that attain this bound. Furthermore, we define the local Laplacian energy of a graph and establish its relationship with the Laplacian energy of the graph.