论文标题
图形的无标志性拉普拉斯能量的一些新边界
Some new bounds for the signless Laplacian energy of a graph
论文作者
论文摘要
对于简单的图形$ g $，带有$ n $顶点，$ m $ edge和毫无意义的laplacian eigenvalues $ q_ {1} \ geq q_ {2} \ geq \ geq \ cdots \ geq q_ q_ q_ {n} \ geq 0 $ \ sum_ {i = 1}^{n} | q_ {i} - \ bar {d} | $，其中$ \ bar {d} = \ frac {2m} {n} {n} $是$ g $的平均顶点。在本文中，我们获得了两个下限（请参见定理3.1和定理3.2），一个以$ QE（g）$（参见定理3.3）的上限提高了$ QE（g）$的一些已知界限，此外，我们确定了相应的极端图，以实现我们的边界。根据子产品，我们还获得了常规图$ g $的$ QE（g）$的一些界限。
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 $G$.
