Modular Leech Trees of Order at Most 8.

Leach, David

In 1975, John Leech asked when can the edges of a tree on n vertices be labeled with positive integers such that the sums along the paths are exactly the integers 1, 2, . . ., (...). 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 Zk where k = (...) 1 and examined the cases for n ≤ 6. In this paper we show that no modular Leech trees of order 7 exist, and we find all modular Leech trees of order 8.

TREE graphs; GRAPH theory; INTEGERS; PATHS & cycles in graph theory; GRAPH labelings; MATHEMATICAL analysis

International Journal of Combinatorics, 2014, p1

1687-9163

Academic Journal

10.1155/2014/218086