$(13)$ The graph $G$ is shown below.

$($a$)$ Give the incidence matrix.

$($b$)$ List the vertices and give the degree of each.

$($c$)$ Give an example of an eulerian path.

$($d$)$ Give an example of a hamiltonian circuit.

$($e$)$ Give examples of simple circuits of lengths $3,4,5,6,7,$ and $8.$

$($f$)$ Give examples of simple acyclic paths from $1$ to $3$ of lengths $2,3,4,5,6,7.$

$($g$)$ Give an example of an spanning tree.

Figure $1.$ Graph $G.$