WEEK-02 (Optional)

Which of the following adjacency matrices represents a graph that has the same Eulerian path and Hamiltonian path, visiting all nodes and links?

1. $$A=\left[\begin{array}{ccccc}0& 1& 0& 1& 1\\ 1& 0& 1& 1& 0\\ 0& 1& 0& 1& 0\\ 1& 1& 1& 0& 0\\ 1& 0& 0& 0& 0\end{array}\right]$$
2. $$A=\left[\begin{array}{ccccc}0& 1& 0& 0& 1\\ 1& 0& 1& 0& 0\\ 0& 1& 0& 1& 0\\ 0& 0& 1& 0& 1\\ 1& 0& 0& 1& 0\end{array}\right]$$
3. $$A=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\\ 1& 0& 1& 0& 0\\ 0& 1& 0& 1& 0\\ 0& 0& 1& 0& 1\\ 0& 0& 0& 1& 0\end{array}\right]$$
4. $$A=\left[\begin{array}{ccccc}0& 1& 1& 1& 1\\ 1& 0& 1& 1& 1\\ 1& 1& 0& 1& 1\\ 1& 1& 1& 0& 1\\ 1& 1& 1& 1& 0\end{array}\right]$$
5. None of the above

Original idea by: Thaysa Bello