Consider the graph G = , with, V = {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q}.

W = {(A,B), (A,C), (A,D), (B,C), (C,D),(D,E), (E,F), (E,H), (E,I), (F,G), (F,H), (F,I), (G,H), (G,I) (I, J), (J,K), (J,L), (J,M), (J,N), (J,Q), (K,L), (K,M), (K,N), (K,Q), (L,M), (L,N), (L,Q), (M,N), (M,Q), (N,Q)}

1. Considering G as an undirected graph, do the following problems:

h) What is a Clique in a graph? (x2) Identify as many cliques as you can in G.

i) An Articulation Point of G is a node or vertex whose removal disconnects G. Identify the articulation points, if any of G. (x2) Which graph representation is the easiest to use to make this determination?

j) A Bridge of G is an edge whose removal disconnects G. Identify the bridges, if any in G.

k) Trace a Path (or route) from node A to node Q.

l) Modify G into a new graph H, by adding the edges {(I,K), (I,N), (C,E), (D,G), (K,O), (K,P), (M,O), (P,Q)}.

m) Show a Breadth-First Search (BFS) traversal (tour) of H, starting from node A.

n) Show a Depth-First Search (DFS) traversal (tour) of H, starting from node K.

o) A Spanning Tree of a graph is a sub-graph which includes all the nodes of the graph and the sub-graph also forms a tree. (x1) Is the sub-graph formed by the BFS in (1.k) a spanning tree? Explain. (x2) Is the sub-graph formed by the DFS in (1.l) a spanning tree? Explain.

p) Give a binary search tree representation of the edge list of node K in the graph H.