Artículos (Matemática Aplicada I)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10894

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Highly connected star product graphs
(Elsevier, 2006) Marcote, X.; Balbuena, C.; García Vázquez, Pedro; Valenzuela, J. C.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Educación y Ciencia (MEC). España
In this work we approach the connectivity κ of a kind of product graphs that were introduced by J.C. Bermond et al. in 1984. More precisely, we provide lower bounds for κ, and state sufficient conditions that guarantee these product graphs to be maximally connected or superconnected. A main consequence is that even graphs with low connectivity may lead to highly connected larger (product) graphs.
Edge-connectivity and edge-superconnectivity in sequence graphs
(Elsevier, 2007) Balbuena, C.; Fàbrega, J.; García Vázquez, Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Educación y Ciencia (MEC). España
Given an integer k 1 and any graph G, the sequence graph Sk(G) is the graph whose set of vertices is the set of all walks of length k in G. Moreover, two vertices of Sk(G) are joined by an edge if and only if their corresponding walks are adjacent in G. In this paper we prove sufficient conditions for a sequence graph Sk(G) to be maximally edge-connected and edgesuperconnected depending on the parity of k and on the vertex-connectivity of the original graph G.
Counterexample to a conjecture of Gyori on C-2l-free bipartite graphs
(North Holland (Elsevier), 2007) Balbuena, C.; García Vázquez, Pedro; Marcote, X.; Valenzuela, J. C.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Educación y Ciencia (MEC). España
A counterexample on a conjecture of Györi related with C2l -free bipartite graphs is described
On the order of ({r, m}; g)-cages of even girth
(North Holland (Elsevier), 2008) Araujo-Pardo, G.; Balbuena, C.; García Vázquez, Pedro; Marcote, X.; Valenzuela, J. C.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
By an ({r, m}; g)-cage we mean a graph on a minimum number of vertices f({r, m}; g) with degree set {r, m}, 2 r
Connectivity measures in matched sum graphs
(North Holland (Elsevier), 2008) Balbuena, C.; García Vázquez, Pedro; Marcote, X.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
A matched sum graph G of two graphs G1 and G2 of the same order is obtained from the union of G1 and G2 and from joining each vertex of G1 with one vertex of G2 according to one bijection f between the vertices in V(G1) and V(G2). When G1 =G2 =H then f is just a permutation of V(H) and the corresponding matched sum graph is a permutation graph H f . In this paper, we derive lower bounds for the connectivity, edge-connectivity, and different conditional connectivities in matched sum graphs, and present sufficient conditions which guarantee maximum values for these conditional connectivities.
A sufficient condition for P-k-path graphs being r-connec
(Elsevier, 2007) Balbuena, C.; García Vázquez, Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Given an integer k 1 and any graph G, the path graph Pk(G) has for vertices the paths of length k in G, and two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of length k − 1 in G, and their union forms either a cycle or a path of length k + 1. Path graphs were investigated by Broersma and Hoede [Path graphs, J. Graph Theory 13 (1989), 427–444] as a natural generalization of line graphs. In fact, P1(G) is the line graph of G. For k = 1, 2 results on connectivity of Pk(G) have been given for several authors. In this work, we present a sufficient condition to guarantee that Pk(G) is connected for k 2 if the girth of G is at least (k + 3)/2 and its minimum degree is at least 4. Furthermore, we determine a lower bound of the vertex-connectivity of Pk(G) if the girth is at least k + 1 and the minimum degree is at least r + 1 where r 2 is an integer.
Superconnectivity of graphs with odd girth g and even girth h
(Elsevier, 2010) Balbuena, C.; García Vázquez, Pedro; Montejano, L. P.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
A maximally connected graph of minimum degree δ is said to be superconnected (for short super-κ) if all disconnecting sets of cardinality δ are the neighborhood of some vertex of degree δ. Sufficient conditions on the diameter to guarantee that a graph of odd girth g and even girth h ≥ g + 3 is super-κ are stated. Also polarity graphs are shown to be super-κ.
On the lambda '-optimality in graphs with odd girth g and even girth h
(Pergamon, 2011) Balbuena, C.; García Vázquez, Pedro; Montejano, L. P.; Salas, J.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
For a connected graph G, the restricted edge-connectivity λ′(G) is defined as the minimum cardinality of an edge-cut over all edge-cuts S such that there are no isolated vertices in G−S. A graph G is said to be λ′-optimal if λ′(G) = ξ (G), where ξ (G) is the minimum edgedegree in G defined as ξ (G) = min{d(u)+d(v)−2 : uv ∈ E(G)}, d(u) denoting the degree of a vertex u. The main result of this paper is that graphs with odd girth g and finite even girth h ≥ g +3 of diameter at most h−4 are λ′-optimal. As a consequence polarity graphs are shown to be λ′-optimal.
On the Superconnectivity in graphs with odd girth g and even girth h
(Elsevier, 2009) Montejano, Luis Pedro; Balbuena, C.; García Vázquez, Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
A maximally connected graph G of minimum degree δ is said to be superconnected (for short super-κ) if all disconnecting sets of cardinality δ are the neighborhood of some vertex of degree δ. Sufficient conditions on the diameter to guarantee that a graph of odd girth g and even girth h ≥ g + 3 is super-κ are stated. Also polarity graphs are shown to be super-κ.
Edge fault tolerance analysis of super k-restricted connected networks
(Elsevier, 2010) Balbuena, C.; García Vázquez, Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
An edge cut X of a connected graph G is a k-restricted edge cut if G X is disconnected and every component of G X has at least k vertices. Additionally, if the deletion of a minimum k-restricted edge cut isolates a connected component of k vertices, then the graph is said to be super-kk. In this paper, several sufficient conditions yielding super-kk graphs are given in terms of the girth and the diameter.
Conditional Diameter Saturated Graphs
(Wiley, 2008) Balbuena, C.; García Vázquez, Pedro; Marcote, X.; Valenzuela, J. C.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
The conditional diameter DP (G) of a connected graph G is a measure of the maximum distance between two subsets of vertices satisfying a given property P of interest. For any given integer k ≥ 1, a connected graph G is said to be conditional diameter k -saturated if D (G) ≥ k and there does not exist any other connected P graph G_ with order |V (G_ )| = |V (G)|, size |E(G_ )| > |E(G)|, and conditional diameter DP (G_ ) ≥ k . In this article, we obtain such conditional diameter saturated graphs for a number of properties P, generalizing the results obtained in (Ore, J Combin Theory 5(1968), 75–81) for the (standard) diameter D(G). )| > |E(G)|, and conditional diameter DP (G ) ≥ k . In this article, we obtain such conditional diameter saturated graphs for a number of properties P, generalizing the results obtained in (Ore, J Combin Theory 5(1968), 75–81) for the (standard) diameter D(G).
Some remarks on avalanches modelling: an introduction to shallow flows models
(Springer, 2014) Fernández Nieto, Enrique Domingo; Vigneaux, Paul; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
The main goal of these notes is to present several depth-averaged models with application in granular avalanches. We begin by recalling the classical Saint-Venant or Shallow Water equations and present some extensions like the Saint-Venant–Exner model for bedload sediment transport. The first part is devoted to the derivation of several avalanche models of Savage–Hutter type, using a depth-averaging procedure of the 3D momentum and mass equations. First, the Savage–Hutter model for aerial avalanches is presented. Two other models for partially fluidized avalanches are then described: one in which the velocities of both the fluid and the solid phases are assumed to be equal, and another one in which both velocities are unknowns of the system. Finally, a Savage–Hutter model for submarine avalanches is derived. The second part is devoted to non-newtonian models, namely viscoplastic fluids. Indeed, a one-phase viscoplastic model can also be used to simulate fluidized avalanches. A brief introduction to Rheology and plasticity is presented in order to explain the Herschel–Bulkley constitutive law. We finally present the derivation of a shallow Herschel–Bulkley model.
Restricted arc-connectivity of generalized p-cycles
(Elsevier, 2012) Balbuena, C.; García Vázquez, Pedro; Hansberg, A.; Montejano, L. P.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
For a strongly connected digraph D the restricted arc-connectivity λ′(D) is defined as the minimum cardinality of an arc-cut over all arc-cuts S satisfying that D − S has a non-trivial strong component D1 such that D − V(D1) contains an arc. In this paper we prove that a generalized p-cycle is λ′-optimal if diam(D) ≤ 2ℓ + p − 2, where ℓ is the semigirth of D and p ≥ 3. Further we show that the k-iterated line digraph is λ′-optimal if diam(D) ≤ 2ℓ + p − 2 + k for p ≥ 3. We improve these results for p large enough and we also improve known results on super-λ for p-cycles with p ≥ 3.
On the Super-Restricted Arc-Connectivity of s-Geodetic Digraphs
(Wiley, 2013) Balbuena, Camino; García Vázquez, Pedro; Hansberg, Adriana; Montejano, Luis Pedro; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Numerical simulation of the 30_45 ka debris avalanche flow of Montagne Pelee volcano, Martinique: from volcano flank collapse to submarine emplacement
(Springer, 2017) Brunet, Morgane; Moretti, Laurent; Le Friant, Anne; Mangeney, Anne; Fernández Nieto, Enrique Domingo; Bouchut, Francois; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
We simulate here the emplacement of the debris avalanche generated by the last flank collapse event of Montagne Pele´e volcano (30–45 ka), Martinique, Lesser Antilles. Our objective is to assess the maximum distance (i.e., runout) that can be reached by this type of debris avalanche as a function of the volume involved. Numerical simulations are performed using two complementary depth-averaged thin-layer continuum models because no complete models were available in the literature. The first model, SHALTOP, accurately describes dry granular flows over a 3D topography and may be easily extended to describe submarine avalanches. The second model, HYSEA, describes the subaerial and submarine parts of the avalanche as well as its interaction with the water column. However, HYSEA less accurately describes the thin-layer approximation on the 3D topography. Simulations were undertaken testing different empirical friction laws and debris avalanche volume flows. Our study suggests that large collapses (*25 km3) probably occurred in several times with successive volumes smaller than about 5 km3 entering the sea. This result provides new constraints on the emplacement processes of debris avalanches associated with these collapses which can drastically change the related hazard assessment such as the generated tsunami, in a region known for its seismic and volcanic risks.
The general set in the MOM isotopic model
(Springer, 2005) Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Geometría y Topología
To obtain a bigger number of mathematical and physical applications of the Santilli’s isotheory, the latest studies have shown the necessity of analyzing isotopic models which use non associative laws. The main goal of this paper is to give a generalization of the isotopic construction model based on the multiplication (MCIM), which is useful to obtain non associative mathematical isostructures.
Numerical and experimental validation of the solar radiation transfer for an egg-crate shading device under Mediterranean climate conditions
(Pergamon-Elsevier, 2019) Domínguez Torres, Carlos Antonio; León-Rodríguez, Ángel Luis; Suárez, Rafael; Domínguez Delgado, Antonio; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Estructuras de Edificación e Ingeniería del Terreno; Universidad de Sevilla. Departamento de Construcciones Arquitectónicas I (ETSA)
Future global warming scenarios will have a significant influence on existing building, especially in those most vulnerable due to major percentages of glazed area. Increasing temperatures will result in an increase in energy consumption due to cooling, especially in the Mediterranean climate with high solar radiation levels. Sun protection systems may be one of the first strategies employed to resolve this issue. Among these, bidirectional shading devices display an excellent behavior although its numerical simulation is very difficult. This research aims to develop an open source numerical method to calculate the short wave solar transmittance in an egg-crate shading device for use in the rehabilitation of tertiary buildings in Mediterranean climate. For this purpose a dynamic three-dimensional hybrid model has been developed combining raytracing and radiosity methods. The numerical method has been validated with monitoring data in southern Spain. The results obtained confirmed the accuracy of the model and the suitability of this type of shading devices in reducing the solar gains in summer with reduced blocking of solar radiation in winter.
Colouring games based on autotopisms of Latin hyper-rectangles
(Taylor & Francis, 2019) Andres, Stephan Dominique; Falcón Ganfornina, Raúl Manuel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Every partial colouring of a Hamming graph is uniquely related to a partial Latin hyper-rectangle. In this paper we introduce the -stabilized (a; b)- colouring game for Hamming graphs, a variant of the (a; b)-colouring game so that each move must respect a given autotopism of the resulting partial Latin hyper- rectangle. We examine the complexity of this variant by means of its chromatic number. We focus in particular on the bi-dimensional case, for which the game is played on the Cartesian product of two complete graphs, and also on the hypercube case.
Classifying partial Latin rectangles
(Elsevier, 2015) Falcón Ganfornina, Raúl Manuel; Stones, Rebecca J.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Isotopisms of the set Rr,s,n of r × s partial Latin rectangles based on n symbols constitute a finite group that acts on this set by permuting rows, columns and symbols. The number of partial Latin rectangles preserved by this action only depends on the conjugacy classes of these permutations. In this paper, the distribution of the isotopism group into conjugacy classes is considered in order to determine the distribution of Rr,s,n into isomorphism and isotopism classes, for all r, s, n ≤ 6.
Autotopism stabilized colouring games on rook's graphs
(Elsevier, 2019) Falcón Ganfornina, Raúl Manuel; Andres, Stephan Dominique; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
This paper deals with the Θ-stabilized colouring game on the n × n rook’s graph, which constitutes a variant of the classical colouring game on finite graphs so that each configuration of the game is uniquely related to a partial Latin square of order n that respects a given autotopism Θ. The complexity of this variant is examined by means of its Θ-stabilized game chromatic number, whose currently known upper bound is improved to 2n−1. Particularly, we introduce the concept of a passing board that enables us to describe a constructive method to compute this number. Based on this method, we explicitly determine the game chromatic number associated to those n × n rook’s graphs, for which n ≤ 4.

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