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A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvari proved the existence of integral trees of any even diameter. In the odd case, int...
Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees
Sub-Gaussian tail conditioned Galton--Watson trees
2010/11/23
We study the height and width of a Galton--Watson tree with offspring distribution B satisfying E(B)=1, 0 < Var(B) < infinity, conditioned on having exactly n nodes. Under this conditioning, we deriv...
Star graphs: threaded distance trees and E-sets
Star graphs threaded distance trees E-sets
2010/11/22
The distribution of distances in the star graph $ST_n$, ($1established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given...