Consider graphs G and H as depicted in the attached paper. a) (2 marks) Are the two graphs isomorphic? If yes, specify the mapping f from the set of nodes in G to the set of nodes in H that preserves all the edges. If no, exhibit a property that holds in one of the graphs but not in the other. b) (1 mark) Is the graph H bipartite? If yes, label its nodes with R (Red) and B (Blue), such that no nodes colored with the same color are connected by an edge. If no, explain why a Red-Blue coloring is not possible. c) (2 marks) Determine the vertex connectivity k(G). Specify a separating set with k(G) vertices. d) (2 marks) Transform graph H into a directed graph by assigning some direction to each edge in H such that the resulting directed graph has two strongly connected components. Specify what are the two strongly connected components. e) (2 marks) List all simple paths of length at most 4 between vertex a and vertex g in graph H. 2 6 7 8 5 3 4 G a le g