Algebraic Properties and Panconnectivity of Folded Hypercubes

Abstract

This paper considers the folded hypercube \(FQ_n\) as an enhancement on the hypercube, and obtains some algebraic properties of \(FQ_n\). Using these properties, the authors show that for any two vertices \(x\) and \(y\) in \(FQ_n\), with distance \(d\) and any integers \(h \in \{d, n+1- d\}\) and \(l\) with \(h \leq l \leq 2^n – 1\), \(FQ_n\) contains an \(xy\)-path of length \(l\) and no \(xy\)-path of other length, provided that \(l\) and \(h\) have the same parity.