Hamiltonian cycle
has the awaited property with regard to the connectivity.
-\begin{Theo}
+\begin{thrm}
The iteration graph $\Gamma(f)$ issued from
the ${\mathsf{N}}$-cube where an Hamiltonian
cycle is removed is strongly connected.
-\end{Theo}
+\end{thrm}
Moreover, if all the transitions have the same probability ($\frac{1}{n}$),
we have proven the following results:
-\begin{Theo}
+\begin{thrm}
The Markov Matrix $M$ resulting from the ${\mathsf{N}}$-cube in
which an Hamiltonian
cycle is removed, is doubly stochastic.
-\end{Theo}
+\end{thrm}
Let us consider now a ${\mathsf{N}}$-cube where an Hamiltonian
cycle is removed.
The answer is indeed positive. We furtheremore have the following strongest
result.
-\begin{Theo}
+\begin{thrm}
There exist $b \in \Nats$ such that $\Gamma_{\{b\}}(f)$ is complete.
-\end{Theo}
+\end{thrm}
\begin{proof}
There is an arc $(x,y)$ in the
graph $\Gamma_{\{b\}}(f)$ if and only if $M^b_{xy}$ is positive
