Reports de recerca http://hdl.handle.net/2117/3742 2021-12-08T07:17:48Z Boundary value problems for Schrödinger operators on a path http://hdl.handle.net/2117/16111 Boundary value problems for Schrödinger operators on a path Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia In this work, we concentrate on determining explicit expressions, via suitable orthogonal polynomials on the line, for the Green function associated with any regular boundary value problem on a weighted path, whose weights are determined by the coefficients of the three terms recurrence relation defining the polynomials. Our study is similar to what is known for boundary value problems associated with ordinary differential equations. 2012-06-21T08:55:34Z Carmona Mejías, Ángeles Encinas Bachiller, Andrés Marcos Gago Álvarez, Silvia In this work, we concentrate on determining explicit expressions, via suitable orthogonal polynomials on the line, for the Green function associated with any regular boundary value problem on a weighted path, whose weights are determined by the coefficients of the three terms recurrence relation defining the polynomials. Our study is similar to what is known for boundary value problems associated with ordinary differential equations. Betweenness-selfcentric graphs http://hdl.handle.net/2117/15768 Betweenness-selfcentric graphs Gago Álvarez, Silvia; Hurajová, Jana; Madaras, Tomas The betweenness centrality of a vertex of a graph is the portion of shortest paths between all pairs of vertices passing through that vertex. In this paper, we study properties and constructions of graphs whose vertices have the same value of betweenness centrality. 2012-05-02T08:54:06Z Gago Álvarez, Silvia Hurajová, Jana Madaras, Tomas The betweenness centrality of a vertex of a graph is the portion of shortest paths between all pairs of vertices passing through that vertex. In this paper, we study properties and constructions of graphs whose vertices have the same value of betweenness centrality. Jacobi matrices and boundary value problems in distance-regular graphs http://hdl.handle.net/2117/14821 Jacobi matrices and boundary value problems in distance-regular graphs Bendito Pérez, Enrique; Carmona Mejías, Ángeles; Encinas Bachiller, Andrés Marcos; Gago Álvarez, Silvia In this work we analyze regular boundary value problems on a distance-regular graph associated with SchrÄodinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the distance polynomials of the distance-regular graphs. 2012-01-26T10:21:55Z Bendito Pérez, Enrique Carmona Mejías, Ángeles Encinas Bachiller, Andrés Marcos Gago Álvarez, Silvia In this work we analyze regular boundary value problems on a distance-regular graph associated with SchrÄodinger operators. These problems include the cases in which the boundary has two or one vertices. Moreover, we obtain the Green matrix for each regular problem. In each case, the Green matrices are given in terms of two families of orthogonal polynomials one of them corresponding with the distance polynomials of the distance-regular graphs.