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- W2950994869 abstract "For positive integers $jge k$, an $L(j,k)$-labeling of a digraph $D$ is a function $f$ from $V(D)$ into the set of nonnegative integers such that $|f(x)-f(y)|ge j$ if $x$ is adjacent to $y$ in $D$ and $|f(x)-f(y)|ge k$ if $x$ is of distant two to $y$ in $D$. Elements of the image of $f$ are called labels. The $L(j,k)$-labeling problem is to determine the $vec{lambda}_{j,k}$-number $vec{lambda}_{j,k}(D)$ of a digraph $D$, which is the minimum of the maximum label used in an $L(j,k)$-labeling of $D$. This paper studies $vec{lambda}_{j,k}$- numbers of digraphs. In particular, we determine $vec{lambda}_{j,k}$- numbers of digraphs whose longest dipath is of length at most 2, and $vec{lambda}_{j,k}$-numbers of ditrees having dipaths of length 4. We also give bounds for $vec{lambda}_{j,k}$-numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining $vec{lambda}_{j,1}$-numbers of ditrees whose longest dipath is of length 3." @default.
- W2950994869 created "2019-06-27" @default.
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- W2950994869 date "2004-07-09" @default.
- W2950994869 modified "2023-10-18" @default.
- W2950994869 title "Distance-two labelings of digraphs" @default.
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