Israel Rocha - Academia.edu (original) (raw)
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Fujian Agriculture and Forestry University, China
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Papers by Israel Rocha
Electronic Notes in Discrete Mathematics, 2011
We study a subfamily -which we call A q -of the family of trees known as caterpillars. We show th... more We study a subfamily -which we call A q -of the family of trees known as caterpillars. We show that all but one tree in A q is a type II tree. We give bounds for the algebraic connectivity in A q and exhibit the tree attaining the bounds. Finally we give a total order in A q by algebraic connectivity.
Linear Algebra and Its Applications, 2011
Given an n-vertex graph G = (V, E), the Laplacian spectrum of G is the set of eigenvalues of the ... more Given an n-vertex graph G = (V, E), the Laplacian spectrum of G is the set of eigenvalues of the Laplacian matrix L = D − A, where D and A denote the diagonal matrix of vertex-degrees and the adjacency matrix of G, respectively. In this paper, we study the Laplacian spectrum of trees. More precisely, we find a new upper bound on the sum of the k largest Laplacian eigenvalues of every n-vertex tree, where k ∈ {1, . . . , n}. This result is used to establish that the n-vertex star has the highest Laplacian energy over all n-vertex trees, which answers affirmatively to a question raised by Radenković and Gutman .
Electronic Notes in Discrete Mathematics, 2011
We study a subfamily -which we call A q -of the family of trees known as caterpillars. We show th... more We study a subfamily -which we call A q -of the family of trees known as caterpillars. We show that all but one tree in A q is a type II tree. We give bounds for the algebraic connectivity in A q and exhibit the tree attaining the bounds. Finally we give a total order in A q by algebraic connectivity.
Linear Algebra and Its Applications, 2011
Given an n-vertex graph G = (V, E), the Laplacian spectrum of G is the set of eigenvalues of the ... more Given an n-vertex graph G = (V, E), the Laplacian spectrum of G is the set of eigenvalues of the Laplacian matrix L = D − A, where D and A denote the diagonal matrix of vertex-degrees and the adjacency matrix of G, respectively. In this paper, we study the Laplacian spectrum of trees. More precisely, we find a new upper bound on the sum of the k largest Laplacian eigenvalues of every n-vertex tree, where k ∈ {1, . . . , n}. This result is used to establish that the n-vertex star has the highest Laplacian energy over all n-vertex trees, which answers affirmatively to a question raised by Radenković and Gutman .