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.