On two energy-like invariants of line graphs and related graph operations

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• 作者：Xiaodan Chen ; Yaoping Hou ; Jingjian Li
• 关键词：05C50 ; 05C90 ; Laplacian ; energy ; like invariant ; incidence energy ; line graph ; subdivision graph ; para ; line graph ; total graph
• 刊名：Journal of Inequalities and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,630 KB
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• 作者单位：Xiaodan Chen (1) (2)
  Yaoping Hou (2)
  Jingjian Li (1)
  
  1. College of Mathematics and Information Science, Guangxi University, Daxue Road 100, Nanning, 530004, P.R. China
  2. Department of Mathematics, Hunan Normal University, Lushan Road 36, Changsha, 410081, P.R. China
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

For a simple graph G of order n, let \(\mu_{1}\geq\mu_{2}\geq\cdots\geq\mu_{n}=0\) be its Laplacian eigenvalues, and let \(q_{1}\geq q_{2}\geq\cdots\geq q_{n}\geq0\) be its signless Laplacian eigenvalues. The Laplacian-energy-like invariant and incidence energy of G are defined as, respectively, $$\mathit{LEL}(G)=\sum_{i=1}^{n-1}\sqrt{ \mu_{i}} \quad\mbox{and}\quad \mathit {IE}(G)=\sum_{i=1}^{n} \sqrt{q_{i}}. $$