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Maxima of the Q-index: degenerate graphs | | V. Nikiforov
; | | Date: |
19 Sep 2013 | | Abstract: | Let G be a k-degenerate graph of order n. It is known that e(G) <=
e(S_{n,k}), where S_{n,k} is the join of a complete graph of order k and an
independent set of order n-k. In this note it is shown that mu(G) <=
mu(S_{n,k}) and q(G) <= q(S_{n,k}). where mu(H) and q(H) stand for the largest
eigenvalues of the adjacency matrix and the signless Laplacian of a graph H.
The latter inequality is deduced from an upper bound on q(G), which is of its
own interest and improves some known upper bounds on q(G). | | Source: | arXiv, 1309.4837 | | Services: | Forum | Review | PDF | Favorites | |
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