NEED HELP Question $2$: Is a graph a tree? A tree is a graph $($V$,$ E$)$ with two special properties: $-$ Every vertex has at most one incoming edge. $-$ Either there are no vertices, or there is a vertex with no incoming edges, called the root, from which all other vertices are reachable. If the second property does not hold, incidentally, the graph is called a forest. Write an is$\_$tree property that has value True if the graph is a tree, and has value False otherwise. Implementation of tree test $[36]$ #@itle Implementation of tree test def graph$\_$is$\_$tree$($self$)$: if len$($graph$.$edges$)!=$ len$($graph$.$vertices$)-1$: return False incoming$\_$edges $=\{\}$ for edge in graph.edges: $\_,$ v$=$ edge if v in incoming$\_$edges: return False incoming$\_$edges$[$v$]=$ True root$\_$exists $=$ False for vertex in graph.vertices: if vertex not in incoming$\_$edges: if root$\_$exists: return False root$\_$exists $=$ True $[36]$ #@title Implementation of tree test def graph$\_$is$\_$tree$($self$)$: if len$($graph$.$edges$)!=$len$($g r a p h $.$ v e r t i c e s$)-1$: return False incoming$\_$edges $=\{\}$ for edge in graph.edges: $-,$ v$=$ edge if v in incoming$\_$edges: return False incoming$\_$edges $[$v$]=$ True root$\_$exists $=$ False for vertex in graph.vertices: if vertex not in incoming$\_$edges: if root$\_$exists: return False root$\_$exists $=$ True return True Graph.is$\_$tree $=$ property $($graph$\_$is$\_$tree$)$# You may want to write tests here. #YOUR CODE HERE $37]$ ### $15$ points: Tests for tree. g$=$Graph$($ vertices $=[1,2,3],$ edges $=[(1,2),(1,3)])$ assert true $($g$.$is tree$)$ g$=$Graph $($vertices $=[1,2,3],$ edges $=[(1,2),(2,3),(1,3)])$ assert$\_$false$($g$.$is$\_$tree$)$ g$=$Graph $($vertices $=[1,2,3],$ edges $=[(1,3),(2,3)])$ assert$\_$false$($g$.$is$\_$tree$)$ g$=$Graph$(.$ vertices$=[\text{'}$a$\text{'},\text{'}$b$\text{'}],$ edges $=[(\text{'}$ a $\text{'},\text{'}$ b$^\text{'})])$ assert$\_$true $($g$.$is$\_$tree$)$ g $=$ Graph$($vertices$=[\text{'}$a$\text{'},\text{'}$b$\text{'}],$ edges$=[(\text{'}$a$\text{'},\text{'}$b$\text{'}),(\text{'}$b$\text{'},\text{'}$a$\text{'})])$ assert$\_$false$($g$.$is$\_$tree$)$ NameError $3$g$=$Graph $($vertices $=[1,2,3],$ edges $=[(1,2),(1,3)])4$ assert$\_$true$($g$.$is$\_$tree$)56$g$=$Graph $($vertices $=[1,2,3],$ edges $=[(1,2),(2,3),(1,3)])$ipython$-$input$-36-4504196$f$0$ba$8>$ in graph$\_$is$\_$tree$($self$)23$ def graph$\_$is$\_$tree$($self$)$: $4$ if len$($graph$.$edges$)!=$ len$($graph$.$vertices$)-1$ : $5$ return False $6$ NameError: name 'graph' is not defined SEARCH STACK OVERFLOW