Advanced Search

We study two topological properties of the 5-ary $n$-cube $Q_n^5$. Given two arbitrary distinct nodes $x$ and $y$ in $Q_n^5$, we prove that there exists an $x$-$y$ path of every length ranging from $2n$ to $5^n-1$, where $n\ge 2$. Based on this result, we prove that $Q_n^5$ is 5-edge-pancyclic by showing that every edge in $Q_n^5$ lies on a cycle of every length ranging from $5$ to $5^n$.

We study two topological properties of the 5-ary -cube $Q_n^5$. Given two arbitrary distinct nodes and in $Q_n^5$, we prove that there exists an - path of every length ranging from to 5 - 1, where ≥ 2. Based on this result, we prove that $Q_n^5$ is 5-edge-pancyclic by showing that every edge in $Q_n^5$ lies on a cycle of every length ranging from to 5.