Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Strongly distance-balanced graphs and graph products

A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given

Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

Content aggregation on knowledge bases using graph clustering

Recently, research projects such as PADLR and SWAP have developed tools like Edutella or Bibster, which are targeted at establishing peer-to-peer knowledge management (P2PKM) systems. In such a system, it is necessary to obtain provide brief semantic descriptions of peers, so that routing algorithms or matchmaking processes can make decisions about which communities peers should belong to, or to which peers a given query should be forwarded. This paper proposes the use of graph clustering techniques on knowledge bases for that purpose. Using this clustering, we can show that our strategy requires up to 58% fewer queries than the baselines to yield full recall in a bibliographic P2PKM scenario.

Understanding Subsystems in Biology through Dimensionality Reduction, Graph Partitioning and Analytical Modeling

Biological systems exhibit rich and complex behavior through the orchestrated interplay of a large array of components. It is hypothesized that separable subsystems with some degree of functional autonomy exist; deciphering their independent behavior and functionality would greatly facilitate understanding the system as a whole. Discovering and analyzing such subsystems are hence pivotal problems in the quest to gain a quantitative understanding of complex biological systems. In this work, using approaches from machine learning, physics and graph theory, methods for the identification and analysis of such subsystems were developed. A novel methodology, based on a recent machine learning algorithm known as non-negative matrix factorization (NMF), was developed to discover such subsystems in a set of large-scale gene expression data. This set of subsystems was then used to predict functional relationships between genes, and this approach was shown to score significantly higher than conventional methods when benchmarking them against existing databases. Moreover, a mathematical treatment was developed to treat simple network subsystems based only on their topology (independent of particular parameter values). Application to a problem of experimental interest demonstrated the need for extentions to the conventional model to fully explain the experimental data. Finally, the notion of a subsystem was evaluated from a topological perspective. A number of different protein networks were examined to analyze their topological properties with respect to separability, seeking to find separable subsystems. These networks were shown to exhibit separability in a nonintuitive fashion, while the separable subsystems were of strong biological significance. It was demonstrated that the separability property found was not due to incomplete or biased data, but is likely to reflect biological structure.

L'entrevista: Gabriel, escultor. "L'art té sentit, no significat"

Som a Palau de Santa Eulàlia, a la casa taller de l'escultor Gabriel. És autor de l’escultura De Profundis al frontispici de la Facultat d’Educació i Psicologia i de l’Escola Universitària d’Infermeria. Comença l'entrevista mentre sona un carilló mogut pel vent. Tot i l'anarquia del seus moviments, els sons que produeix els apercebem com una melodia

[Ressenya del llibre Els nous horitzons culturals a Mallorca al final de l'Edat Mitjana, de Maria Barceló i Gabriel Ensenyat]

Ressenya del llibre Els nous horitzons culturals a Mallorca al final de l'Edat Mitjana, de Maria Barceló i Gabriel Ensenyat. L’obra tracta sobre l’humanisme a Mallorca, la conclusió de la qual és que, tenint en compte que l’humanisme en estat pur no va existir ni tan sols a Itàlia, es pot parlar de l’humanisme català comptant amb les seves reminiscències de l’Edat Mitjana de les que no se sostreuen enlloc

[Ressenya del llibre Francesc Fontanella: una obra, una vida, un temps, de Pep Valsalobre i Gabriel Sansano (eds.)]

Comentari del llibre Francesc Fontanella: una obra, una vida, un temps. Es tracta d’una obra miscel•lània en la que es recullen, partits en dos àmbits temàtics, un històric i un literari, 14 assaigs sobre temes que van des dels fets centrals de la Guerra dels Segadors fins a una proposta per a la realització d’una obra teatral fontanelliana

Web Graph

Slides and an essay on the Web Graph, search engines and how Google calculates Page Rank

Graph Theory and Social Networks Tutorial

For COMP60

Gabriel Comas i Ribas : la seva vida i obra. 'Gabriel Comas i Ribas : su vida y obra'.

Se trata de una aproximación a la figura del profesor Gabriel Comas i Ribas (Esporles, 1864- Barcelona, 1942) y al contexto en el que éste desarrolló su actividad docente, a finales del siglo XIX y principios del siglo XX. Comas destacó por su dinamismo pedagógico y educativo, en linea con la renovación pedagógica y la corriente pestalozziana, que le llevó a proporcionar diversas y numerosas aportaciones a la historia de la pedagogía de las Islas Baleares. Desarrolló su profesión en diversos centros de Mallorca y Menorca hasta recalar en 1905 en Palma, donde su experiencia e inquietudes educativas le llevaron a transformar la escuela de Santa Catalina en Escuela Graduada, a potenciar el papel social de la escuela y promover el desarrollo integral del ser humano. Tras un viaje por el extranjero para profundizar en las teorías pedagógicas del momento, desarrolló una intensa etapa como conferenciante y realizó numerosos escritos en la revista El Magisterio Balear, teorizando sobre la situación de la pedagogía en nuestro país y de los distintos países que visitó. En 1923 se traslada a la Escuela Unitaria número 69 de Barcelona, donde se jubiló en 1934.

Gabriel Coll i Mulet, mestre Guillemet. 'Gabriel Coll Mulet, el maestro Guillemet'.

Se presenta la biografía del maestro Guillemet, que fue maestro de Santa Eugenia entre 1929 y 1936, desarrollando una tarea extraordinaria para elevar la formación y la cultura no tan sólo del alumnado sino también de la población adulta de la localidad. Era un hombre dedicado, ilusionado por mejorar la educación y la cultura de sus conciudadanos pero sufrió la amargura de la incomprensión y la intolerancia, pues la injusticia de la depuración del servicio y la cárcel, a causa de la Guerra Civil, lo apartaron de la enseñanza, a la que no volvió posteriormente. El volumen se inicia con el contexto histórico y pedagógico, las raíces y la formación pedagógica de Gabriel Coll. A continuación se relatan los primeros destinos y valoraciones a cargo de la Inspección Educativa, la enseñanza en Santa Eugenia antes de 1929 y la tarea que él desarrolló. Se comenta la existencia de un protector, Pere Coll Bibiloni y, en el plano personal, su matrimonio con Magdalena Pons i Palou, también maestra e igualmente depurada. Se analiza la práctica docente desarrollada por este maestro a partir del cuestionario escolar a antiguos alumnos y los recuerdos actuales de éstos. Se describe también el proceso para dar el nombre de este profesional a la escuela de la localidad. El volumen incluye un annexo documental.