(c) Let si denote an independent set on{v1,…,v1} , and let xi denote its weight. Define x0= 0 and note that x1= w1. Now, for I >1 ,either vi belongs to si or it doesn’t. In the first case ,we know that vi-1 cannot belong to si,and so xi = wi + xi-2. In the second case , xi= xi-1. Thus we have the recurrence
Xi = man(xi-1 ,wi + xi-2).