Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph Theory,68(2), October 2011, 169-176], have shown that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cycle, where 3<=j<=5 if i=3 and 4<=j<=6 if i=4. We improve the above mentioned result and prove that every planar graph without an i-cycle adjacent to a j-cycle with3<=j<=5 if i=3 and 4<=j<=5 if i=4 is acyclically 5-choosable.

Edge-choosability of Planar Graphs

According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable.

Conceptual Analysis of Web 2.0 Technology Use to Enhance Parent–School Relationships

Parent–school relationships contribute significantly to the quality of students’ education. The Internet, in turn, has started to influence individuals’ way social communication and most school boards in Ontario now use the Internet to communicate with parents, which helps build parent–school relationships. This project comprised a conceptual analysis of how the Internet enhances parent–school relationships to support Ontario school board administrators seeking to implement such technology. The study’s literature review identified the links between Web 2.0 technology, parent–school relationships, and effective parent engagement. A conceptual framework of the features of Web 2.0 tools that promote social interaction was developed and used to analyze websites of three Ontario school boards. The analysis revealed that school board websites used static features such as email, newsletters, and announcements for communication and did not provide access to parents for providing feedback through Web 2.0 features such as instant messaging. General recommendations were made so that school board administrators have the opportunity to implement changes in their school community with feasible modifications. Overall, Web 2.0-based technologies such as interactive communication tools and social media hold the most promise for enhancing parent–school relationships because they can help not only overcome barriers of time and distance, but also improve the parents’ desire to be engaged in children’s education experiences.

Properties and Algorithms of the KCube Graphs

The KCube interconnection topology was rst introduced in 2010. The KCube graph is a compound graph of a Kautz digraph and hypercubes. Compared with the at- tractive Kautz digraph and well known hypercube graph, the KCube graph could accommodate as many nodes as possible for a given indegree (and outdegree) and the diameter of interconnection networks. However, there are few algorithms designed for the KCube graph. In this thesis, we will concentrate on nding graph theoretical properties of the KCube graph and designing parallel algorithms that run on this network. We will explore several topological properties, such as bipartiteness, Hamiltonianicity, and symmetry property. These properties for the KCube graph are very useful to develop efficient algorithms on this network. We will then study the KCube network from the algorithmic point of view, and will give an improved routing algorithm. In addition, we will present two optimal broadcasting algorithms. They are fundamental algorithms to many applications. A literature review of the state of the art network designs in relation to the KCube network as well as some open problems in this field will also be given.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.

Using PageRank Algorithm in Analyzing Dictionary Graphs and PageRank in Dynamic Graphs

In this thesis we are going to analyze the dictionary graphs and some other kinds of graphs using the PagerRank algorithm. We calculated the correlation between the degree and PageRank of all nodes for a graph obtained from Merriam-Webster dictionary, a French dictionary and WordNet hypernym and synonym dictionaries. Our conclusion was that PageRank can be a good tool to compare the quality of dictionaries. We studied some artificial social and random graphs. We found that when we omitted some random nodes from each of the graphs, we have not noticed any significant changes in the ranking of the nodes according to their PageRank. We also discovered that some social graphs selected for our study were less resistant to the changes of PageRank.

Diagrams (charts and graphs) made into a booklet with a newspaper cover

Diagrams (charts and graphs) made into a booklet with a newspaper cover. This booklet contains cross sections of the back ditch on the south side of the Welland Canal feeder, west of the Marshville culverts (45 pages, hand drawn). This was created by Fred Holmes, Oct. 3, 1857.

Charts and graphs of cross sections from Brown’s ditch culvert to the main drain

Charts and graphs of cross sections from Brown’s ditch culvert to the main drain, cross sections from the feeder on the road allowance between lots 26 and 27 in the 5th concession of Humberstone, Cross sections of the main drain from Lyons Creek culvert to the road allowance between lots 7 and 8 in Wainfleet and cross selections of the old ditch on the west side of the road allowance between lots 17 and 18 in the 3rd concession in Wainfleet (8 pages, hand drawn), n.d.

Análisis, administración y control de inventarios en empresas de manufactura (Un enfoque conceptual)

Tesis ( Maestría en Administración con Especialidad en Finanzas) U.A.N.L.

Aplicación de las finanzas en la toma de decisiones: (Enfoque conceptual )

[Tesis] ( Maestría en Administración con Especialidad en Finanzas) U.A.N.L.

La estadística como herramienta conceptual para la solución de problemas en el área de contaduría y administración.

Tesis (Maestría en Enseñanza de las Ciencias con Especialidad en Matemáticas) UANL, 2009.

Medidas implícitas y pre-atentivas de la representación conceptual de la autoestima y del autoconcepto.

Tesis (Doctorado en Filosofía con Especialidad en Psicología) UANL, 2011.

Une approche conceptuelle pour l’interprétation des graphiques en cinématique au secondaire

Cette recherche tente de déterminer si, dans le cadre d’un cours de physique de cinquième secondaire, l’utilisation d’un laboratoire par enquête guidée (comme complément d’enseignement basé sur une approche conceptuelle) permet aux élèves de mieux comprendre des notions de cinématique, que le laboratoire traditionnel. Elle s’inscrit dans une série d’études, réalisées au collégial ou à l’université, qui portent sur des approches d’enseignement exploitant le laboratoire comme moyen de transmission des concepts mécaniques en physique (McDermott, 1996; Beichner, 1994). Le laboratoire par enquête est associé à une approche conceptuelle axée sur le raisonnement qualitatif alors que celui qui est traditionnel est associé à une approche traditionnelle de l’enseignement de la physique. Le test TUG-K, «Test of Understanding Graphs in Kinematics » (Beichner, 1994), ainsi que des entrevues individuelles ont été utilisés afin d’évaluer la compréhension des concepts de cinématique. Il semble d’abord que le laboratoire par enquête guidé soit efficace pour enseigner la plupart des notions de cinématique. De plus, en comparant deux groupes d’une trentaine d’élèves de 5e secondaire ayant suivi deux types de laboratoires différents, l’étude a permis d’entrevoir une piste concernant la compréhension du concept d’accélération. Les résultats suggèrent qu’un laboratoire associé à une approche conceptuelle permettrait aux étudiants, à long terme, de mieux s’approprier les notions d’accélération qu’un laboratoire traditionnel.

Towards the identification of a neighbourhood park typology : a conceptual and methodological exploration

Peu d’études ont évalué les caractéristiques des parcs pouvant encourager l’activité physique spécifiquement chez les jeunes. Cette étude vise à estimer la fiabilité d’un outil d’observation des parcs orienté vers les jeunes, à identifier les domaines conceptuels des parcs capturés par cet outil à l’aide d’une opérationnalisation du modèle conceptuel des parcs et de l’activité physique et à identifier différents types de parcs. Un total de 576 parcs ont été évalués en utilisant un outil d’évaluation des parcs. La fiabilité intra-juges et la fiabilité inter-juges de cet outil ont été estimées. Une analyse exploratoire par composantes principales (ACP) a été effectuée en utilisant une rotation orthogonale varimax et les variables étaient retenues si elles saturaient à ≥0.3 sur une composante. Une analyse par grappes (AG) à l’aide de la méthode de Ward a ensuite été réalisée en utilisant les composantes principales et une mesure de l’aire des parcs. L’outil était généralement fiable et l’ACP a permis d'identifier dix composantes principales qui expliquaient 60% de la variance totale. L’AG a donné un résultat de neuf grappes qui expliquaient 40% de la variance totale. Les méthodes de l’ACP et l’AG sont donc faisables avec des données de parcs. Les résultats ont été interprétés en utilisant l’opérationnalisation du modèle conceptuel.