@article {
author = {Nayak, Nutan},
title = {On net-Laplacian Energy of Signed Graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {2},
number = {1},
pages = {11-19},
year = {2017},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2017.13578},
abstract = {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 $\Sigma$ 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. },
keywords = {Net-regular signed graph,net-Laplacian matrix,net-Laplacian energy},
url = {http://comb-opt.azaruniv.ac.ir/article_13578.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13578_7e090ec81543bab5c2a566524067cc39.pdf}
}