On net-Laplacian Energy of Signed Graphs

Document Type : Original paper

Author

S.S.Dempo College of Commerce and Economics, Altinho, Panaji,Goa

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. 

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References

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Communications in Combinatorics and Optimization
Volume 2, Issue 1
June 2017
Pages 11-19

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