Resumen de L(1,1)-Labeling of Direct Product of any Path and cycle

Deborah Olayide Ajayi, Charles Adefokun

• Suppose that [n] = {0, 1, 2,...,n} is a set of non-negative integers and h,k G [n].The L (h, k)-labeling of graph G is the function l : V(G) — [n] such that |l(u) — l(v)| > h if the distance d(u,v) between u and v is 1 and |l(u) — l(v)| > k if d(u,v) = 2. Let L(V(G)) = {l(v): v G V(G)} and let p be the maximum value of L(V(G)). Then p is called Xi^—number of G if p is the least possible member of [n] such that G maintains an L(h, k) — labeling. In this paper, we establish X} — numbers of Pm X Pn and Pm X Cn graphs for all m,n > 2.