Exercise $1.$ Traversals

Let G be a graph with $8$ nodes labeled A$,$ B$,$ C$,$ D$,$ E$,$ F$,$ H$,$ J$,$ and let the adjacent nodes of each node be as follows:

$A(B,C,D),B(A,C,D),C(A,B,D),D(A,B,C,F),E(F,H,J),F(D,E,H),H(E,F,J),H(E,H)$

a$)$ Draw G$.$ Also show the adjacency matrix for G$.$

b$)$ On a copy of G$,$ label the nodes with numbers $1.\mathrm{.}8$ to show the order in which they would be visited in a DFS traversal starting at node A$.$ Also, show which are the discovery edges by making them red and directed $($alternately$,$ make them thicker rather than red$).$

NOTE: for your traversals, assume that the adjacent nodes of any given node are returned in the same order as they are listed above.

c$)$ On a copy of G$,$ label the nodes with numbers $1.\mathrm{.}8$ to show the order in which they would be visited in a BFS traversal starting at node A$.$ Also, show which are the discovery edges by making them red and directed $($alternately$,$ make them thicker rather than red$).$

NOTE: the discovery edges should form a tree rooted at A$,$ aka search tree.