On cyclic decompositions of the complete graph into the bipartite generalized Petersen graph P(n,3)

Abstract

A uniformly-ordered ρ-labeling (also known as a ρ++-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 K2mt+1 for every positive integer t. Here we show that for every even integer n≥8, the generalized Petersen graph P(n,3) admits a ρ++-labeling and hence cyclically decomposes K6nt+1 for all positive integers t.