$/**$

$*$ Determines whether an undirected graph is bipartite

$*$ @param g an undirected graph

$*$ @param bipartite is true if g is bipartite, otherwise false

$*$ @return an array of size $|$G$|+1.$ The first entry is $|$G$|$ and the remaining

$*$ entries are in $\{0,1\}$ when g is bipartite where $[$i$]=1$ if vertex i

$*$ is in the first partition and $0$ if it is in the second partition;

$*$ if g is not bipartite null returned.

$*/$

private static int$[]$ isBipartite$($Graph g$,$ AtomicBoolean bipartite$)$ throws GraphException

$\{$

$//$Implement this method

return null;

$\}```$

$/**$

$*$ Determines whether an undirected graph is bipartite

$*$ @param g an undirected graph

$*$ @param bipartite is true if g is bipartite, otherwise false

$*$ @return an array of size $|$G$|+1.$ The first entry is $|$G$|$ and the remaining

$*$ entries are in $\{0,1\}$ when g is bipartite where $[$i$]=1$ if vertex i

$*$ is in the first partition and $0$ if it is in the second partition;

$*$ if g is not bipartite null returned.

$*/$

private static int$[]$ isBipartite$($Graph g$,$ AtomicBoolean bipartite$)$ throws GraphException

$\{$

$//$Implement this method

return null;

$\}$

$/**$

$*$ an auxiliary method for the topoSort method.

$*$ @param g a weighted directed graph

$*$ @param v current vertex

$*$ @param seen a $1-$D boolean matrix of vertices that

$*$ have been marked.

$*$ @param linearOrder a $1-$D array containing the

$*$ topologically sorted list.

$*$ @param index current index.

$*/$

private static void dfs$0$ut$($Graphg$\_$ int v$/$ boolean seen$[],$ int linearOrder$[],$AtomicInteger index$)$ throws GraphException

$\{$

$//$implement this method

$\backslash$

$/**$

$*$ This method generates a listing of the vertices of a weighted

$*$ directed graph using the reverse dfs topological sorting.

$*$ @param g a weighted directed graph

$*$ @return an array containing a topological ordering of the vertices

$*$ of g in reverse DFS order; Null is returned if the g

$*$ contains a directed cycle

$*/$

private static int$[]$ topoSort$($Graph g$)$ throws GraphException

$\{$

$//$implement this method

return null;

$\}$

$```$