And increased knowledge of the human understanding of how the operation of the physical world surroundings. through controlled methods

A combinatorial bijection between k-edge colored trees and colored Pr¨ufer codes for labelled trees is established. This bijection gives a simple combinatorial proof for the number k(n − 2)!nk−n n−2
of k-edge colored trees with n vertices.A k-edge colored tree is a labelled tree whose edges are colored from a set of k colors such that any two edges with a common vertex have different colors

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It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at least 2pd − 1 cos(  2k ). A similar result has been proved by Friedman using more sophisticated tools.More generally, Serre has shown (see [3], [4] ) that for any fixed r and for any infinite family of d-regular graphs Gi, lim inf r(Gi) 2pd − 1. The same result has been proved by Friedman already in [5].

4p thulanh5 12-09-2011 97 6   Download