Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 218086, 2 pages
http://dx.doi.org/10.1155/2014/218086
Research Article

Modular Leech Trees of Order at Most 8

Department of Mathematics, University of West Georgia, 1601 Maple Street, Carrollton, GA 30118, USA

Received 11 August 2014; Accepted 2 September 2014; Published 18 September 2014

Academic Editor: Laszlo A. Szekely

Copyright © 2014 David Leach. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In 1975, John Leech asked when can the edges of a tree on vertices be labeled with positive integers such that the sums along the paths are exactly the integers . He found five such trees, and no additional trees have been discovered since. In 2011 Leach and Walsh introduced the idea of labeling trees with elements of the group where and examined the cases for . In this paper we show that no modular Leech trees of order 7 exist, and we find all modular Leech trees of order 8.