Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site watmath.UUCP Path: utzoo!watmath!ljdickey From: ljdickey@watmath.UUCP (Lee Dickey) Newsgroups: net.math Subject: A graph theory question Message-ID: <5448@watmath.UUCP> Date: Sun, 26-Jun-83 19:51:09 EDT Article-I.D.: watmath.5448 Posted: Sun Jun 26 19:51:09 1983 Date-Received: Mon, 27-Jun-83 00:26:39 EDT Sender: ljdickey@watmath.UUCP Organization: U of Waterloo, Ontario Lines: 39 About a week or so ago, I passed along an example of two graphs that had the same set of leaf distances, but which were not isomorphic. Here is another pair of graphs, discovered to Prof. J. Michael Robinson, smaller than the previous example, which have that same property: o o | | o------------o o------------o | / \ | / \ o o o o o o / \ | | / \ | | o o o o o o o o Each of these graphs has: 1 pair of leaves with distance 2 2 pairs of leaves with distance 3 3 pairs of leaves with distance 4 4 pairs of leaves with distance 5. Prof. Ronald C. Read has discovered the smallest (counting the number of vertices) example of a pair of graphs that have the same distance sequences, but which are not isomorphic: o o o o o \ / \|/ o--o--o o | | o o / \ | o o o / \ /|\ o o o o o Each of these graphs has: 6 pairs of leaves with distance 2 9 pairs of leaves with distance 4. It is interesting to note that they have different numbers of vertices.