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- Germain Pastén, Oscar Rojo

Let G be a simple, undirected, connected and finite graph. with the pendent vertices of K 1,si. It is proved that (i) if µ ̸ = 0 and µ ̸ = 1 is a Laplacian eigenvalue of G, then µ is a Laplacian eigenvalue of G(H 1 ,. .. , H r) and (ii) for 1 ≤ i ≤ r, if µ is a Laplacian eigenvalue of H i , µ ̸ = 0 or µ = 0 with an eigenvector orthogonal to the all ones… (More)

- Oscar Rojo
- Computers & Mathematics with Applications
- 2008

Bose-Einstein condensation (BEC) in two dimensions (2D) (e.g., to describe the quasi-2D cuprates) is suggested as the possible mechanism widely believed to underlie superconduc-tivity in general. A crucial role is played by nonzero center-of-mass momentum Cooper pairs (CPs) usually neglected in BCS theory. Also vital is the unique linear dispersion relation… (More)

A caterpillar is a tree in which the removal of all pendent vertices make it a path. In this paper, we consider two classes of caterpillars. We present an ordering of caterpillars by algebraic connectivity in one of them and find one that maximizes the algebraic connectivity in the other class.

- OSCAR ROJO, LUIS MEDINA
- 2009

A generalized Bethe tree is a rooted tree in which vertices at the same distance from the root have the same degree. Let Gm be a connected weighted graph on m vertices. Let (iii) the edges of B i joining the vertices at the level j with the vertices at the level (j + 1) have weight w i,k i −j for j = 1, 2,. .. , k i − 1. Let Gm {B i : 1 ≤ i ≤ m} be the… (More)

- Oscar Rojo, Luis Medina, Nair Abreu, Claudia Justel
- Electronic Notes in Discrete Mathematics
- 2009

Let G be a simple undirected connected graph on n vertices. Suppose that the vertices of G are labelled 1,2,... ,n. Let d i be the degree of the vertex i. The Randi´c matrix of G , denoted by R, is the n × n matrix whose (i, j) − entry is 1 √ d i d j if the vertices i and j are adjacent and 0 otherwise. The normalized Laplacian matrix of G is L = I − R,… (More)

- Oscar Rojo
- 2007

Let G = (V (G), E(G)) be a unicyclic simple undirected graph with largest vertex degree. Let C r be the unique cycle of G. The graph G − E(C r) is a forest of r rooted trees T 1 , T k(G) = max 1ir {max{dist(v i , u) : u ∈ V (T i)}} + 1, where dist(v, u) is the distance from v to u. Let μ 1 (G) and λ 1 (G) be the spectral radius of the Laplacian matrix and… (More)

A caterpillar is a tree in which the removal of all pendant vertices makes it a path. Let d ≥ 3 and n ≥ 6 be given. Let P d−1 be the path of d − 1 vertices and Sp be the star of p + 1 vertices. In this paper, the caterpillars in C and in S having the maximum and the minimum algebraic connectivity are found. Moreover, the algebraic connectivity of a… (More)

- Oscar Rojo, Israel Rocha, Vilmar Trevisan
- Electronic Notes in Discrete Mathematics
- 2011