A linear algorithm for the grundy number of a tree

A coloring of a graph G = (V,E) is a partition {V1, V2, . . ., Vk} of V into independent sets or color classes. A vertex v Vi is a Grundy vertex if it is adjacent to at least one vertex in each color class Vj . A coloring is a Grundy coloring if every color class contains at least one Grundy vertex, and the Grundy number of a graph is the maximum number of colors in a Grundy coloring. We derive a natural upper bound on this parameter and show that graphs with sufficiently large girth achieve equality in the bound. In particular, this gives a linear time algorithm to determine the Grundy number of a tree

On The Equality Of The Grundy Numbers Of A Graph

Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. Thus the problem of stability of the network ad hoc which corresponds to a problem of allocation of frequency amounts to a problem of allocation of colors in the vertex of graph. we present use a parameter of coloring the number of Grundy. The Grundy number of a graph G, denoted by (G), is the largest k such that G has a greedy k-coloring, that is a coloring with colours obtained by applying the greedy algorithm according to some ordering of the vertices of G. In this paper, we study the Grundy number of the lexicographic, Cartesian and direct products of two graphs in terms of the Grundy numbers of these graphs.Comment: 13 pages, International Journal of Next-Generation Networks (IJNGN),December 201

Use of Multi-Watermarking Schema to Maintain Awareness in a Teleneurology Diagnosis Platform

Following the tremendous evolution of transferring images through the Internet, it is necessary to ensure security during this act, especially for medical images. The application of multiple watermarking tech- nique represents a solution to preserve the security of such data on the one hand, and the traceability of medical diagnoses made by doctors on the other hand. This falls under the remote collaborative work. This technique is applied in the TeNeCi (Collaborative tele-neurology) platform. The project allows practitioners to distribute the analyses of the medical images. In fact, we used the multiple watermarking technique in a wavelet field. The theory underlying this technique is to hide information in the medical image and at the same time to ensure its imperceptibility. The diagnosis made by the practitioner is the data inserted in the image. The fundamental challenge of this paper is how to hide the total diagnoses of each practitioner in the image ensuring a good quality of the image at the same time