Some new bounds for the signless Laplacian energy of a graph
| Autor: | Wang, Peng, Huang, Qiongxiang |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a simple graph $G$ with $n$ vertices, $m$ edges and signless Laplacian eigenvalues $q_{1} \geq q_{2} \geq \cdots \geq q_{n} \geq 0$, its the signless Laplacian energy $QE(G)$ is defined as $QE(G) = \sum_{i=1}^{n}|q_{i} - \bar{d} |$, where $\bar{d} = \frac{2m}{n}$ is the average vertex degree of $G$. In this paper, we obtain two lower bounds ( see Theorem 3.1 and Theorem 3.2 ) and one upper bound for $QE(G)$ ( see Theorem 3.3 ), which improve some known bounds of $QE(G)$, and moreover, we determine the corresponding extremal graphs that achieve our bounds. By subproduct, we also get some bounds for $QE(G)$ of regular graph $G$. Comment: 19 pages |
| Databáze: | arXiv |
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