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 difference 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 Σ is defined as ε(L(Σ)) = Σn i=1 |γi − 2m /n | where γ1, γ2, . . . , γn are the eigenvalues of L(Σ) and 2m n is the average degree of the vertices in Σ. In this paper, we define 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.