(b) Let G be the graph on vertices V1, V2, .., V8 with the following adjacency matrix: 01 000001 10100001 0 1 0 0 1 0 0 1 0 0 0 0 0 110 0 0 100000 0 0 0 10 000 00010000 100000 1 1 i. Use the connectedness algorithm to find the connected component of V1. ii. Sketch all the graphs (up to isomorphism) on four vertices that are isomorphic to an induced subgraph of G (identifying a suitable induced subgraph in each case). iii. Sketch all the graphs (up to isomorphism) on four vertices that are not iso- morphic to an induced subgraph of G. iv. Find a graph on four vertices that is isomorphic to a subgraph, but not to an induced subgraph, of G. Explain your answer.

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