Samuel Jurkiewicz

The characteristic polynomial of the Laplacian of graphs in (a,b)-linear classes

In this work we deal with the characteristic polynomial of the Laplacian of a graph. We present some general results about the coefficients of this polynomial. We present families of graphs, for which the number of edges m is given by a linear function of the number of vertices n. In some of these graphs we can find certain coefficients of the above-named polynomial as functions just of n.

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.

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.

Independent Production of Non Hamiltonian Graphs

Abstract The decision whether a graph is hamiltonian or not is known to be an NP-complete problem. The importance of this kind of problem motivate several researchers in heuristics development. However, problems arise in the evaluating of this heuristics, more often because it is difficult to produce independent data. In this paper we develop methods to produce non hamiltonian graphs, based on independence subsets and toughness arguments. We also present a family of non hamiltonian graphs with strong restrictions, that is, planar 1-tough non hamiltonan graphs with no separation triangles.

The Fifth and Sixth Coefficients of the Characteristic Polynomial of a Graph

Abstract It is well known that the coefficients of the characteristic polynomial of a graph G are determined by the elementary subgraphs of G ; in particular there are simple expressions for the four higest coefficients. Here we use an enumeration of elementary subgraphs called k -matchings to obtain expressions for the next two coefficients.