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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].

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Collection of research reports best university in 2008 honored the author: 1. Housing Ta Khac Luong Quoc Tuyen Nguyen Thi Thu Ha, Le Thi Ngoc, the probability measure functor preserving some topological properties that ... science (Scientia, in Latin, meaning "knowledge" or "understanding") is the efforts to implement the invention, and increased knowledge of the human understanding of how the operation of the physical world around them.

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Collection of research reports best universities honored author. Two. Le Van Dung, a number average convergence theorem for two index array of random elements in Banach spaces with integrable conditions are ... Science (in Latin Scientia, meaning "knowledge "or" understanding ") is the efforts to implement the invention, and increased knowledge of the human understanding of how the operation of the physical world around them.

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