On net-Laplacian Energy of Signed Graphs

A signed graph is a graph where the edges are assigned either positive or negative signs. Net degree of a signed graph is the dierence between the number of positive and negative edges incident with a vertex. It is said to be net-regular if all its vertices have the same net-degree. Laplacian energy of a signed graph  is defined as ε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the eigenvalues of L(Σ) and (2m)/n is the average degree of the vertices in Σ. In this paper, we dene net-Laplacian matrix considering the edge signs of a signed graph and give bounds for signed net-Laplacian eigenvalues. Further, we introduce net-Laplacian energy of a signed graph and establish net-Laplacian energy bounds.