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From: jcn@aplvax.UUCP
Newsgroups: net.math
Subject: A graph theory question
Message-ID: <110@aplvax.UUCP>
Date: Thu, 9-Jun-83 14:06:13 EDT
Article-I.D.: aplvax.110
Posted: Thu Jun  9 14:06:13 1983
Date-Received: Fri, 10-Jun-83 01:38:13 EDT
Lines: 22


This problem deals strictly with tree graphs.

Define a "distance sequence" as a sequence of numbers that are the
distances between all unique pairs of leaves in a tree (leaves 
are points of degree 1). 

For example, the distance sequence for a tree with 2 points is <1>,
while the distance sequence for the tree with 3 points is <2>,
the distance sequence for the star graph 4 points is <2,2,2>.

The question:

	If two trees have the same distance sequence, must they
be automorphic (i.e. the same tree)? That is, does a distance
sequence uniquely define a tree?

					John Noble
					Johns Hopkins Applied Physics Lab
					Laurel, Md 20707
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