Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!linus!genrad!decvax!harpo!seismo!rlgvax!cvl!umcp-cs!aplvax!jcn 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 ...rglvax!umcp-cs!aplvax!jcn ...decvax!harpo!seismo!umcp-cs!aplvax!jcn