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Your search keyword '"SAFE, MARTÍN D."' showing total 29 results
Start Over Author "SAFE, MARTÍN D." Publisher elsevier b.v.
29 results on '"SAFE, MARTÍN D."'

21. Computing the Determinant of the Distance Matrix of a Bicyclic Graph.

Author

Grippo, Luciano N., Safe, Martín D., da Silva, Celso M., Del-Vecchio, Renata R., and Dratman, Ezequiel

Subjects
GRAPH connectivity, MATRICES (Mathematics), DISTANCES, EUCLIDEAN distance
Abstract

Let G be a connected graph with vertex set V = { v 1 ,..., v n }. The distance d (v i , v j) between two vertices v i and v j is the number of edges of a shortest path linking them. The distance matrix of G is the n × n matrix such that its (i , j)-entry is equal to d (v i , v j). A formula to compute the determinant of this matrix in terms of the number of vertices was found when the graph either is a tree or is a unicyclic graph. For a byciclic graph, the determinant is known in the case where the cycles have no common edges. In this paper, we present some advances for the remaining cases; i.e., when the cycles share at least one edge. We also present a conjecture for the unsolved cases. [ABSTRACT FROM AUTHOR]

Published
2019
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27. The determinant of the distance matrix of graphs with blocks at most bicyclic.

Author

Dratman, Ezequiel, Grippo, Luciano N., Safe, Martín D., da Silva, Celso M., and Del-Vecchio, Renata R.

Subjects
*GRAPH connectivity, *TREE graphs, *MATRICES (Mathematics), *DISTANCES, *SPANNING trees
Abstract

Let G be a connected graph on n vertices and D (G) be its distance matrix. The formula for computing the determinant of this matrix in terms of the number of vertices is known when the graph is either a tree or a unicyclic graph. In this work we generalize these results, obtaining the determinant of the distance matrix of any graph whose block decomposition consists of edges, unicyclic and bicyclic graphs. [ABSTRACT FROM AUTHOR]

Published
2021
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28. A {−1,0,1}- and sparsest basis for the null space of a forest in optimal time.

Author

Jaume, Daniel A., Molina, Gonzalo, Pastine, Adrián, and Safe, Martín D.

Subjects
*CLASSIFICATION algorithms, *MATHEMATICS theorems, *NUMERICAL solutions to functional equations, *GEOMETRIC vertices, *VECTOR algebra
Abstract

Given a matrix, the Null Space Problem asks for a basis of its null space having the fewest nonzeros. This problem is known to be NP-complete and even hard to approximate. The null space of a forest is the null space of its adjacency matrix. Sander and Sander (2005) and Akbari et al. (2006), independently, proved that the null space of each forest admits a { − 1 , 0 , 1 } -basis. We devise an algorithm for determining a sparsest basis of the null space of any given forest which, in addition, is a { − 1 , 0 , 1 } -basis. Our algorithm is time-optimal in the sense that it takes time at most proportional to the number of nonzeros in any sparsest basis of the null space of the input forest. Moreover, we show that, given a forest F on n vertices, the set of those vertices x for which there is a vector in the null space of F that is nonzero at x and the number of nonzeros in any sparsest basis of the null space of F can be found in O ( n ) time. [ABSTRACT FROM AUTHOR]

Published
2018
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29. Partial characterizations of circle graphs

Author

Bonomo, Flavia, Durán, Guillermo, Grippo, Luciano N., and Safe, Martín D.

Subjects
*GRAPH theory, *EQUIVALENCE relations (Set theory), *LINEAR statistical models, *MATHEMATICAL analysis, *GRAPHIC methods, *MATHEMATICS
Abstract

Abstract: A circle graph is the intersection graph of a family of chords on a circle. There is no known characterization of circle graphs by forbidden induced subgraphs that do not involve the notions of local equivalence or pivoting operations. We characterize circle graphs by a list of minimal forbidden induced subgraphs when the graph belongs to one of the following classes: linear domino graphs, -tidy graphs, and tree-cographs. We also completely characterize by minimal forbidden induced subgraphs the class of unit Helly circle graphs, which are those circle graphs having a model whose chords have all the same length, are pairwise different, and satisfy the Helly property. [Copyright &y& Elsevier]

Published
2011
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