On labeling the vertices of products of complete graphs with distance constraints

Variations of Hale's channel assignment problem, the L(j, k)-labeling problem and the radio labeling problem require the assignment of integers to the vertices of a graph G subject to various distance constraints. The lambda(j,k)-number of G and the radio number of G are respectively the minimum span among all L((j,k))-labelings, and the number span plus 1 of all radio labelings of G (defined in the Introduction). In this paper, we establish the lambda(j,k)-number of Pi(i)(a) = (1) K-1 for pairwise relatively prime integers t(1) < t(2) < ... < t(q), t(1) greater than or equal to 2. We also show the existence of an infinite class of graphs G with radio number [V(G)] for any diameter d(G). (C) 2003 Wiley Periodicals, Inc.