$[22$ pts$.]$ Illustrate breadth$-$first search $($BFS$)$ graph traversal on the following simple undirected graph:

Assume that the adjacent vertices of a given vertex are returned in alphabetical order. To complete the illustration, as illustrated during lecture,

$($a$)$ fill$-$in the box next to each vertex with the order number by which the vertices were labeled as "visited" during the respective traversal;

$($b$)$ mark each discovered$/$tree edge with an arrow in the direction in which the edge was discovered;

$($c$)$ mark each cross edge, with an $x$ and an arrow in the direction in which the cross edge was found during the traversal; and

$($d$)$ circle the vertices stored in each of the collections $L_0,L_1,L_2,$ and so on$,$ computed during the traversal, corresponding to the vertices that are in level $0,1,2,$ and so on; and making sure to properly label each collection of vertices.