PLEASE DO ALL PROBLEMS Consider the graph G = <V, W>, with, V = {A, B, C, D, E,

Question

PLEASE DO ALL PROBLEMS

Consider the graph G = <V, W>, 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:

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.

Explanation / Answer

Solution:

Note: The first two subparts have been answered as per Chegg guidelines, please repost others.

1)

k)

The trace is

A-B-C-D-E-F-G-I-K-Q

l)

after adding the new edges the modified graph will have

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), (I,K), (I,N), (C,E), (D,G), (K,O), (K,P), (M,O), (P,Q)}

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.