Problem $4($b$)$

Figure $7$: An undirected graph has $6$ vertices, a through $f.$ There are $9-$line segments that

are between the following vertices: a and $b,$a and $c,$a and $d,$a and $f,b$ and $e,b$ and $f,c$ and

$d,d$ and $e,d$ and $f.($c

Figure $8$: An undirected graph has $5$ vertices, a through e$.$ There are $4-$line segments that are between the following vertices: $b$ and $c,b$ and $e,c$ and $d,d$ and $e.$

Figure $9$: An undirected graph has $7$ vertices, a through g$.$ There are $10-$line segments that are between the following vertices: a and $b,$a and $c,$a and $f,b$ and $c,b$ and $f,c$ and $d,c$ and $g,d$ and $e,d$ and $f,f$ and $g.$

Analyze each graph below to determine whether it has an Euler circuit and$/$or an Euler trail.

If it has an Euler circuit, specify the nodes for one.

If it does not have an Euler circuit, justify why it does not.

If it has an Euler trail, specify the nodes for one.

If it does not have an Euler trail, justify why it does not.

$($a$)$

Figure $6$: An undirected graph has $6$ vertices, a through $f.$ There are $8-$line segments that are between the following vertices: a and $b,$a and $c,$a and $d,$a and $f,b$ and $c,b$ and $e,b$ and $f,d$ and $e.$