## Yoomi Rho (노유미), L(j,k) Labelings of Direct Product of Complete Graphs

L(j,k) labelings of direct product of complete graphs
Yoomi Rho (노유미)
Dept. of Mathematics, Univ. of Incheon, Incheon, Korea.
2011/3/17 Thu 4:30PM-5:30PM (E6-1, Room 3433)
An L(j,k) labeling of a graph is a vertex labeling such that the difference of the labels of any two adjacent vertices is at least j and that of any two vertices of distance 2 is at least k. The minimum of the spans of all L(j,k)-labelings of G is denoted by $$\lambda_k^j(G)$$. Recently Haque and Jha proved if G is a direct product of complete graphs, then $$\lambda_k^j(G)$$ coincide with the trivial lower bound $(N-1)k$ where N is the order of G when j/k is within a certain bound.

In this paper, we suggest a new labeling method of such a graph G. With this method, we extend the range of j/k such that $$\lambda_k^j(G)=(N-1)k$$ holds. Moreover, we obtain an upper bound of $$\lambda_k^j(G)$$ for the remaining cases.

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