Consider a graph with 5 nodes, numbered from 1 through 5. These nodes are connected such that node 1 is connected to node 2, then node 2 is connected to node 3, node 3 is connected to node 4, node 4 is connected to node 5 and node 5 is connected to node 1. so these nodes are forming a pentagon. In addition, node 1 is connected to node 4 and node 2 is connected to node 5. 1. Sketch the graph. Construct the adjacency matrix S that belongs to this graph (see p. 76 of our book). 2. Find the nullspace of S. 3. Compute s? and S. How many walks of length 2 are there betveen node 1 and node 37. How many walks of length 3 are there betveen node 2 and node 4?

Q: Does this have 12 vertices? If not, how does that change the drawing and answers?

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