Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21282120170601On net-Laplacian Energy of Signed Graphs11191357810.22049/cco.2017.13578ENNutan G.NayakS.S.Dempo College of Commerce and Economics, Altinho, Panaji,GoaJournal Article20160828A 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 $Sigma$ is defined as $varepsilon({L} Sigma)) = sum_{i=1}^{n}|gamma_i - frac{2m}{n}|$ where $gamma_{1}, gamma _{2} ,ldots, gamma_{n}$ are the eigenvalues of $L(Sigma)$ and $frac{2m}{n}$ is the average degree of the vertices in $Sigma$. 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. http://comb-opt.azaruniv.ac.ir/article_13578_7e090ec81543bab5c2a566524067cc39.pdf