Leech graphs

Let tp(G) denote the number of paths in a graph G and let f : E -> Z+ be an edge labeling of G. The weight of a path P is the sum of the labels assigned to the edges of P. If the set of weights of the paths in G is {1, 2, 3, ... , tp(G)}, then f is called a Leech labeling of G and a graph which admits a Leech labeling is called a Leech graph. In this paper, we prove that the complete bipartite graphs K2,n and K3,n are not Leech graphs and determine the maximum possible value that can be given to an edge in the Leech labeling of a cycle.