# 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}
}
• 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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