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

Primary and Secondary Education in Morocco: From Access to School into Generalization to Dropout

This article provides an overview of school wastage, namely repetition and dropout in primary and secondary schools in Morocco. It describes how this phenomenon has progressed since school was implemented in the 1960s. It shows that the fundamental principles of the education system established in the aftermath of Morocco’s independence in 1956 did not succeed in providing a clear, stable education program. The article concludes that despite the tremendous efforts made in enrollment, school wastage persists, and the educational system is still trapped in the idealistic principles of the 1960s, causing education to flounder in the dramatic triangle of schooling, generalization, and dropout