# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# $L(j,k)$-Labelings of Direct Products of a Complete Graph and a Cycle

Presented by Dr. Yoomi RHO
Type: Oral presentation
Track: Domination, Independence and Coloring of Product Graphs

## Content

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 span of all $L(j,k)$-labelings of the graph is denoted by $\lambda_k^j$. In 2008, Lin and Lam provided $\lambda_1^2(G)$ for a direct product of a complete graph and a cycle $G$ with special orders. We extend their result for $G$ with other orders. Also we obtain an upper bound of $\lambda_1^1(G)$ for a direct product of a complete graph and a cycle $G$.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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