Since Kronecker Product Graph Model (KPGM) was introduced, it has been widely used to model real networks. The characteristics of the model specially its single fractal structure have made KPGM one of the most important algorithm of the last years. However, the utilization of a single fractal structure decreases the potential of KPGM by limiting the graph space covered by the model. In this pap...

Owing to the inhomogeneity and ill defined edges present in images, the incorporation of prior knowledge into level set models, in image segmentation, is a field of active researches. In this paper, a new way of incorporating prior information to constrain the evolution of the level set model during the segmentation is presented. This technique allows resolving the problem of applying the same ...

This paper is based on a series of talks given at the Patejdlovka Enumeration Workshop held in the Czech Republic in November 2007. The topics covered are as follows. The graph polynomial, Tutte-Grothendieck invariants, an overview of relevant elementary finite Fourier analysis, the Tutte polynomial of a graph as a Hamming weight enumerator of its set of tensions (or flows), description of a fa...

The Shortest Cycle Cover Conjecture of Alon and Tarsi asserts that the edges of every bridgeless graph with m edges can be covered by cycles of total length at most 7m/5 = 1.400m. We show that every cubic bridgeless graph has a cycle cover of total length at most 34m/21 ≈ 1.619m and every bridgeless graph with minimum degree three has a cycle cover of total length at most 44m/27 ≈ 1.630m.

A recent strategy carried out by the aircraft industry to reduce the total cost of the new generation fighters has consisted in the development of a single airframe with different technical and operational specifications. This strategy has been designed to reduce costs in the Research, Design and Development phase with the ultimate objective of reducing the final unit price per aircraft. This i...

In estimating the cost-effectiveness of diagnostic procedures, it is helpful to treat diagnostic information as a commodity with a unit price. The amount of useful information provided by a test result can be measured in binary units (bits), and the unit price of the information produced by the test result can be expressed in dollars per bit in much the same way that the price of gold is given ...

The concept of average degree-eccentricity matrix ADE(G) of a connected graph $G$ is introduced. Some coefficients of the characteristic polynomial of ADE(G) are obtained, as well as a bound for the eigenvalues of ADE(G). We also introduce the average degree-eccentricity graph energy and establish bounds for it.