ON THE LAMBDA-NUMBER OF Q(N) AND RELATED GRAPHS

An L(2, 1)-labeling of graph G is an integer labeling of V(G) such tha t adjacent vertices have labels that differ by at least 2 and such tha t vertices distance 2 apart have labels that differ by at least 1. The lambda-number of G, lambda(G), is the minimum range over all L(2, 1)- labelings. We examine the properties of lambda-labelings of the n-cube Qn. Griggs and Yeh have determined lambda(Q(n)) for n less than or eq ual to 5 and have established n + 3 less than or equal to lambda(Q(n)) less than or equal to 2n+1 for n greater than or equal to 6. We modif y a technique used in coding theory to improve the upper bound. We als o examine the lambda-labelings of related graphs; such as the subdivis ion of the n-cube and the Cartesian products of paths.