Consider the four comb graphs in parts (i), (ii), (iii), and (iv) of Fig 11 96 These graphs have 1 tooth, 2 teeth, 3 teeth, and ft teeth, respectively For n yen 1, let an count the number of independent subsets in x1, x2, , xn, y1, y2, , yn Find and solve a recurrence relation for an x1 x1 x2 x3 (i...

There are two cases to consider 1 The vertex y n is not used Then there are a n1 independent subs ...

Consider the four comb graphs in parts (i), (ii), (iii), and (iv) of Fig. 11.96. These graphs

Question:

Consider the four comb graphs in parts (i), (ii), (iii), and (iv) of Fig. 11.96. These graphs have 1 tooth, 2 teeth, 3 teeth, and ft teeth, respectively. For n ‰¥ 1, let an count the number of independent subsets in {x1, x2, ... , xn, y1, y2, ..., yn}. Find and solve a recurrence relation for an.