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On net-Laplacian Energy of Signed Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 2، شماره 1، شهریور 2017، صفحه 11-19 اصل مقاله (358.05 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2017.13578 | ||
| نویسنده | ||
| Nutan G. Nayak* | ||
| S.S.Dempo College of Commerce and Economics, Altinho, Panaji,Goa | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Net-regular signed graph؛ net-Laplacian matrix؛ net-Laplacian energy | ||
| مراجع | ||
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