$(10$ pts$)$ Consider the following graph $\backslash ($ G $\backslash )$ :

$($a$)(2$ pts$)$ Write out the adjacency list representation for the graph $\backslash ($ G $\backslash ).$ At the list in each node, the vertices connected to it should be in increasing order of vertex number.

$($b$)(6$ pts$)$ Draw the BFS tree resulting from the BFS exploration of the above graph starting from vertex $6.$ Your exploration must consider the neighbors of any vertex in increasing order of vertex number. Show the layer information for each vertex in the BFS tree.

$($c$)(2$ pts$)$ Is the graph a bipartite graph? Justify your answer with an explanation.