Question: (a) Consider the three connected undirected graphs in Fig. 11.11. The graph in part (a) of the figure consists of a cycle (on the vertices

(a) Consider the three connected undirected graphs in Fig. 11.11. The graph in part (a) of the figure consists of a cycle (on the vertices u1, u2, u3) and a vertex u4 with edges (spokes) drawn from u4 to the other three vertices. This graph is called the wheel with three spokes and is denoted by W3. In part (b) of the figure we find the graph W4 - the wheel with four spokes. The wheel W5 with five spokes appears in Fig. 11.11(c). Determine how many cycles of length 4 there are in each of these graphs.
b) In general, if n ˆˆ Z+ and n ‰¥ 3, then the wheel with n spokes is the graph made up of a cycle of length n together with an additional vertex that is adjacent to the n vertices of the cycle. The graph is denoted by Wn. (i) How many cycles of length 4 are there in Wn? (ii) How many cycles in Wn have length n?

U2 U1 Lu Figure 11.11

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