Discrete Mathematics ( IF 0.770 ) Pub Date : 2021-02-22 , DOI: 10.1016/j.disc.2021.112339
Wannasiri Wannasit

A uniformly-ordered $\rho$-labeling (also known as a ${\rho }^{++}$-labeling) of a bipartite graph was introduced by El-Zanati, Vanden Eynden, and Punnim. Such a labeling of a bipartite graph $G$ with $m$ edges yields a cyclic $G$-decomposition of ${K}_{2mt+1}$ for every positive integer $t$. Here we show that for every even integer $n\ge 8$, the generalized Petersen graph $P\left(n,3\right)$ admits a ${\rho }^{++}$-labeling and hence cyclically decomposes ${K}_{6nt+1}$ for all positive integers $t$.

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