Clícia Valladares Peixoto Friedmann

WebQuests, oficinas e guia de orientação: uma proposta integrada para a formação continuada de professores de matemática

This paper presents an integrated proposal for continuing education for mathematics teachers which involved the creation of a site for WebQuest design, interactive workshops and a guide for the use of information and communication technologies in math classes. It describes the development of educational materials integrated with other educational activities, providing a response to the dynamic and complex nature of a teaching-research, and informing the development of an investigation about technologies in the teaching of mathematics. The theoretical framework is based on studies about continuing teacher education, interactivity and education. It explores the emergence of a communicational model that overcomes the transmission and repetition paradigm of the banking pedagogy. Results indicate that continuing teacher education benefits from plural and interactive approaches which promote, within small communities of practice, simultaneous learning about mathematics and its didactics.

Produto funcional de grafos: um modelo para conexão de sistemas multiagentes

Neste trabalho, os conceitos de produto funcional e coloracao total equilibrada em grafos foram utilizados para propor um modelo de conexao entre sistemas multiagentes. Para isso, expomos de forma breve, a ideia de produto funcional, definimos redes de interconexao e sistemas multiagentes, e finalizamos propondo um modelo de conexao entre dois sistemas multiagentes, tomando como base a coloracao total equilibrada e o produto funcional de grafos.

Produto funcional de grafos

O trabalho apresenta uma generalizacao do produto cartesiano de grafos que denominamos de produto funcional, provam-se algumas propriedades do novo produto e mostra-se uma aplicacao do mesmo.

An efficient representation of chordal graphs

Abstract In this paper, a representation for chordal graphs called the compact representation , based on the running intersection property, is presented. It provides the means to immediately deduce several structural properties of a chordal graph such as a perfect elimination ordering, the minimal vertex separators and a clique-tree. These properties support an efficient algorithm for the construction of the compact representation. Simple characterizations of some subclasses of chordal graphs can be obtained using this representation.

Coloração total equilibrada de grafos: um modelo para redes de interconexão

An interconnection network is a structure including a set P of n > 1 processors and a set T of connections of the elements of P, satisfying certain conditions. In this work it will be introduced the concept of equitable total coloring of a graph. This concept is shown to be a natural representation for parallel processing in interconnection networks. For the most common interconnection network topologies an equitable total coloring is presented with at most D +2 colors, thus satisfying a conjecture of Vizing.

RELATIONSHIP BETWEEN EQUITABLE TOTAL COLORING AND RANGE COLORING IN SOME REGULAR GRAPHS

This work aims to study the equitable total coloring into subfamilies of regular graphs. For this purpose, we use some relationships between equitable total coloring and range (vertex) coloring in some regular graphs. The concept of range coloring of order k was first presented by (Lozano et al., 2009). In this paper, we shows that if a regular graph G admits an equitable range coloring c of order Δ with (Δ+1) colors then there is an equitable total coloring of G - with the same set of colors - that extends c. We also show that there are infinite graphs satisfying this theorem. Such graphs are called Harmonics. We generate Harmonic Graphs which are Cartesian products of cycles and their complements. These graphs are regular and they admit an equitable total coloring under the above conditions.

Grafos Block-Cactus são do Tipo 1

O numero cromatico χ T ( G ) de um grafo G e o menor numero de cores necessario para colorir propriamente os vertices e arestas de G . Um grafo que satisfaz a Conjectura da Coloracao Total e dito de tipo 1 se χ T ( G ) = Δ( G ) = 2, onde Δ( G ) e o grau maximo de G . Neste trabalho, apresentamos novos resultados sobre a coloracao total de uma familia de grafos, provando que os grafos block-cactus nao triviais sao do tipo 1.