Maxima of the Q-index: graphs with bounded clique number
| Autor: | de Abreu, Nair Maria Maia, Nikiforov, Vladimir |
|---|---|
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Electronic J. Linear Algebra 23 (2012), 782-789 |
| Druh dokumentu: | Working Paper |
| Popis: | This paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of given order and clique number. More precisely, let G be a graph of order n, let A be its adjacency matrix, and let D be the diagonal matrix of the row-sums of A. If G has clique number r, then the largest eigenvalue q(G) of the matrix Q=A+D satisfies q(G)<= 2(1-1/r)n. If G is a complete regular r-partite graph, then equality holds in the above inequality. This result confirms a conjecture of Hansen and Lucas. Comment: 10 pages, corrected a typo |
| Databáze: | arXiv |
| Externí odkaz: |
|