On the k-restricted edge-connectivity of matched sum graphs

A matched sum graph $G_1$M$G_2$ of two graphs $G_1$ and $G_2$ of the same order n is obtained by adding to the union (or sum) of $G_1$ and $G_2$ a set M of n independent edges which join vertices in V ($G_1$) to vertices in V ($G_2$). When $G_1$ and $G_2$ are isomorphic, $G_1$M$G_2$ is just a permutation graph. In this work we derive bounds for the k-restricted edge connectivity λ(k) of matched sum graphs $G_1$M$G_2$ for 2 ≤ k ≤ 5, and present some sufficient conditions for the optimality of λ(k)($G_1$M$G_2$).Peer Reviewe

Desenvolupament i implementació d´ Unitats Docents Autocontingudes a les assignatures d’Àlgebra

En el curs 2008/2009 s’ha aplicat una metodologia docent nova a l’assignatura d’Àlgebra i Geometria de primer de la titulació d’Enginyeria de Camins. Ha calgut un tipus de material nou que també haurà de servir per a les assignatures d'àlgebra dels nous plans d'estudis. A més del programa de l'assignatura, on s'especifica el contingut dels diferents temes, s’ha treballat amb una programació per "sessions", que corresponen a una hora de classe presencial. Són unitats tancades que permeten dissenyar un calendari atemporal. A l'inici de cada curs acadèmic es concretarà aquest calendari, de manera que l'estudiantat disposarà de la programació detallada de la matèria. Abans de cada sessió l'estudiant ha de treballar els seus continguts i li cal tenir un paper més actiu en el seu aprenentatge. Per aconseguir tot això s'han generat materials nous i rentabiltzat els antics. El projecte ha suposat una primera fase de la readaptació de continguts estàtics i elaboració de nous elements dinàmics amb una organització totalment diferent a la del curs anterior. Així doncs, a partir d'unitats petites, com si fossin peces d'un trencaclosques es podran dissenyar diverses assignatures d'àlgebra, segons el nivell i programa que es vulgui assolir.Peer Reviewe

The p-restricted edge-connectivity of Kneser graphs

© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Given a connected graph G and an integer 1¿=¿p¿=¿¿|V(G)|/2¿, a p-restricted edge-cut of G is any set of edges S¿¿¿E(G), if any, such that is not connected and each component of has at least p vertices; and the p-restricted edge-connectivity of G, denoted ¿p(G), is the minimum cardinality of such a p-restricted edge-cut. When p-restricted edge-cuts exist, G is said to be super-¿p if the deletion from G of any p-restricted edge-cut S of cardinality ¿p(G) yields a graph that has at least one component with exactly p vertices. In this work, we prove that Kneser graphs K(n, k) are ¿p-connected for a wide range of values of p. Moreover, we obtain the values of ¿p(G) for all possible p and all n¿=¿5 when . Also, we discuss in which cases ¿p(G) attains its maximum possible value, and determine for which values of p graph is super-¿p.Peer Reviewe

On the connectivity of semiregular cages

An ({r,r+1};g)-cage is a graph with degree set {r,r+1}, girth g, and with the smallest possible order; every such graph is called a semiregular cage. In this article, semiregular cages are shown to be maximally edge-connected and 2-connected. As a consequence, ({3,4};g)-cages are proved to be maximally connected

Improving bounds on the order of regular graphs of girth 5

© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A -graph is a -regular graph with girth and a -cage is a -graph with the fewest possible number of vertices . Constructing -cages and determining the order are both very hard problems. For this reason, an intensive line of research is devoted to constructing smaller -graphs than previously known ones, providing in this way new upper bounds to each time such a graph is constructed. The paper focuses on girth , where cages are known only for degrees . We construct -graphs using and extending techniques of amalgamation into the incidence graphs of elliptic semiplanes of type introduced and exposed by Funk (2009). The order of these graphs provides better upper bounds on than those known so far, for values of such that either or.Peer Reviewe

Some properties of semiregular cages

A graph with degree set {r,r + 1} is said to be semiregular. A semiregular cage is a semiregular graph with given girth g and the least possible order. First, an upper bound on the diameter of semiregular graphs with girth g and order close enough to the minimum possible value is given in this work. As a consequence, these graphs are proved to be maximally connected when the girth g ≥ 7 is odd. Moreover an upper bound for the order of semiregular cages is given and, as an application, every semiregular cage with degree set {r,r + 1} is proved to be maximally connected for g є {6,8}, and when g = 12 for r ≥ 7 and r ≠ 20. Finally it is also shown that every ({r,r + 1};g)-cage is 3-connected.Postprint (published version

Some properties of semiregular cages

A graph with degree set {r,r + 1} is said to be semiregular. A semiregular cage is a semiregular graph with given girth g and the least possible order. First, an upper bound on the diameter of semiregular graphs with girth g and order close enough to the minimum possible value is given in this work. As a consequence, these graphs are proved to be maximally connected when the girth g ≥ 7 is odd. Moreover an upper bound for the order of semiregular cages is given and, as an application, every semiregular cage with degree set {r,r + 1} is proved to be maximally connected for g є {6,8}, and when g = 12 for r ≥ 7 and r ≠ 20. Finally it is also shown that every ({r,r + 1};g)-cage is 3-connected

On the connectivity of semiregular cages

An ({r,r+1};g)-cage is a graph with degree set {r,r+1}, girth g, and with the smallest possible order; every such graph is called a semiregular cage. In this article, semiregular cages are shown to be maximally edge-connected and 2-connected. As a consequence, ({3,4};g)-cages are proved to be maximally connected

Desenvolupament i implementació d´ Unitats Docents Autocontingudes a les assignatures d’Àlgebra

En el curs 2008/2009 s’ha aplicat una metodologia docent nova a l’assignatura d’Àlgebra i Geometria de primer de la titulació d’Enginyeria de Camins. Ha calgut un tipus de material nou que també haurà de servir per a les assignatures d'àlgebra dels nous plans d'estudis. A més del programa de l'assignatura, on s'especifica el contingut dels diferents temes, s’ha treballat amb una programació per "sessions", que corresponen a una hora de classe presencial. Són unitats tancades que permeten dissenyar un calendari atemporal. A l'inici de cada curs acadèmic es concretarà aquest calendari, de manera que l'estudiantat disposarà de la programació detallada de la matèria. Abans de cada sessió l'estudiant ha de treballar els seus continguts i li cal tenir un paper més actiu en el seu aprenentatge. Per aconseguir tot això s'han generat materials nous i rentabiltzat els antics. El projecte ha suposat una primera fase de la readaptació de continguts estàtics i elaboració de nous elements dinàmics amb una organització totalment diferent a la del curs anterior. Així doncs, a partir d'unitats petites, com si fossin peces d'un trencaclosques es podran dissenyar diverses assignatures d'àlgebra, segons el nivell i programa que es vulgui assolir.Peer Reviewe

The application of a laser range-finding sensor for non-contacting inspection

SIGLELD:D48154/84 / BLDSC - British Library Document Supply CentreGBUnited Kingdo