@Article{CMR-25-1,
author = {Yuan, Wanlian and Zhai, Mingqing and Lü, Changhong},
title = {The $L(3, 2, 1)$-Labeling on Bipartite Graphs},
journal = {Communications in Mathematical Research },
year = {2009},
volume = {25},
number = {1},
pages = {79--87},
abstract = {<p style="text-align: justify;">An $L(3, 2, 1)$-labeling of a graph $G$ is a function from the vertex set $V(G)$ to the set of all nonnegative integers such that $|f(u)−f(v)|≥3$ if $d_G(u, v)=1$, $|f(u)−f(v)|≥2$ if $d_G(u, v)=2$, and $|f(u)−f(v)|≥1$ if $d_G(u, v)=3$. The $L(3, 2, 1)$-labeling problem is to find the smallest number $λ_3(G)$ such that there exists an $L(3, 2, 1)$-labeling function with no label greater than it. This paper studies
the problem for bipartite graphs. We obtain some bounds of $λ_3$ for bipartite graphs
and its subclasses. Moreover, we provide a best possible condition for a tree $T$ such
that $λ_3(T)$ attains the minimum value.</p>},
issn = {2707-8523},
doi = {https://doi.org/2009-CMR-19284},
url = {https://global-sci.com/article/81930/the-l3-2-1-labeling-on-bipartite-graphs}
}