Cyclic base ordering of generalized Petersen graphs

Abstract

A cyclic base ordering (CBO) of a connected graph [Formula: see text] is a cyclic ordering of [Formula: see text] such that every cyclically consecutive [Formula: see text] edge induces a spanning tree of [Formula: see text]. The density of [Formula: see text] is defined to be [Formula: see text]; and [Formula: see text] is uniformly dense if [Formula: see text] for every connected subgraph [Formula: see text] of [Formula: see text]. It was conjectured by Kajitani, Ueno and Miyano that [Formula: see text] has a CBO if and only if [Formula: see text] is uniformly dense. In this paper, we study CBO of generalized Petersen graphs to support this conjecture, and we prove that [Formula: see text] and [Formula: see text] have CBO.