A lower bound for the sum of the two largest signless Laplacian eigenvalues

@article{Oliveira2014ALB,
  title={A lower bound for the sum of the two largest signless Laplacian eigenvalues},
  author={Carlos Sousa Oliveira and Leonardo Silva de Lima},
  journal={Electron. Notes Discret. Math.},
  year={2014},
  volume={55},
  pages={173-176}
}
  • Carlos Sousa Oliveira, Leonardo Silva de Lima
  • Published in
    Electron. Notes Discret. Math…
    2014
  • Computer Science, Mathematics
  • Let $G$ be a graph of order $n \geq 3$ with sequence degree given as $d_{1}(G) \geq ... \geq d_{n}(G)$ and let $\mu_1(G),..., \mu_n(G)$ and $q_1(G), ..., q_{n}(G)$ be the Laplacian and signless Laplacian eigenvalues of $G$ arranged in non increasing order, respectively. Here, we consider the Grone's inequality [R. Grone, Eigenvalues and degree sequences of graphs, Lin. Multilin. Alg. 39 (1995) 133--136] $$ \sum_{i=1}^{k} \mu_{i}(G) \geq \sum_{i=1}^{k} d_{i}(G)+1$$ and prove that for $k=2$, the… CONTINUE READING

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