Maria Aguieiras A. de Freitas

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Let G be a graph with two non adjacent vertices and G′ the graph constructed from G by adding an edge between them. It is known that the trace of Q′ is 2 plus the trace of Q, where Q and Q′ are the signless Laplacian matrices of G and G′ respectively. So, the sum of the Q′-eigenvalues of G′ is the sum of the the Qeigenvalues of G plus two. It is said that(More)
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 Fn−1 with an edge hanged to its center. It is shown that if G is a graph of order n ≥ 4, with no 4-cycle, then q (G) < q (Fn) , unless G = Fn.(More)
The original graph sandwich problem for a property Π, 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 ⊆ E ⊆ E2 and G satisfies Π (or belongs to a class Π) ? The graph G is called a sandwich graph. The importance of the graph sandwich problem lies in(More)
Taking a Fiedler’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 case(More)
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 speci…ed complete bipartite subgraph. A conjecture is stated about general complete bipartite graphs, which is proved for in…nitely many cases. More precisely, it is(More)
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