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- Maria Aguieiras A. de Freitas, Renata R. Del-Vecchio, Nair Maria Maia de Abreu, Steve Kirkland
- Electronic Notes in Discrete Mathematics
- 2009

Let G be a graph with two non adjacent vertices and Gâ€² the graph constructed from G by adding an edge between them. It is known that the trace of Qâ€² is 2 plus the trace of Q, where Q and Qâ€² are the signless Laplacian matrices of G and Gâ€² respectively. So, the sum of the Qâ€²-eigenvalues of Gâ€² is the sum of the the Qeigenvalues of G plus two. It is said thatâ€¦ (More)

- Maria Aguieiras A. de Freitas, Vladimir Nikiforov, Laura Patuzzi
- 2013

This paper gives tight upper bounds on the largest eigenvalue q (G) of the signless Laplacian of graphs with no 4-cycle and no 5-cycle. If n is odd, let Fn be the friendship graph of order n; if n is even, let Fn be Fnâˆ’1 with an edge hanged to its center. It is shown that if G is a graph of order n â‰¥ 4, with no 4-cycle, then q (G) < q (Fn) , unless G = Fn.â€¦ (More)

- Ruben Hoeksma, Johann Hurink, +11 authors Annie Raymond
- 2013

The original graph sandwich problem for a property Î , as defined by Golumbic, Kaplan, and Shamir, can be stated as follows: given two graphs G1 = (V,E1) and G2 = (V,E2), is there a graph G = (V,E) such that E1 âŠ† E âŠ† E2 and G satisfies Î (or belongs to a class Î ) ? The graph G is called a sandwich graph. The importance of the graph sandwich problem lies inâ€¦ (More)

- Domingos M. Cardoso, Maria Aguieiras A. de Freitas, Enide Andrade Martins, MarÃa Robbiano
- Discrete Mathematics
- 2013

Taking a Fiedlerâ€™s result [1] on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the caseâ€¦ (More)

- Maria Aguieiras A. de Freitas, Vladimir Nikiforovy, Laura Patuzziz
- 2015

This note presents a new spectral version of the graph Zarankiewicz problem: How large can be the maximum eigenvalue of the signless Laplacian of a graph of order n that does not contain a speciÂ…ed complete bipartite subgraph. A conjecture is stated about general complete bipartite graphs, which is proved for inÂ…nitely many cases. More precisely, it isâ€¦ (More)

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