4. (The Petersen graph) Let S = {1, 2, 3, 4, 5}. Let G be a graph with one vertex for each 2-element subset of S and an edge between two vertices if and only if the corresponding subsets of S are disjoint.

a) Draw the graph G and label its vertices with the corresponding subsets of S.

b) Is G regular? If so, of what degree? If not, explain why.

c) Is G bipartite? Justify your claim.

d) Identify a trail of length 5 and a path of length 9 in G