A certain computer algorithm executes three times as many operations when it runs with an input of size k as when it runs with an input of size k - 1 (where k is is an integer greater than 1). When the algorithm is run with an input of size 1, it executes seven operations. Let Sn be the number of operations that the algorithm executes when it runs with an input of size n.
(a) Write a recurrence relation with initial condition to describe the sequence S1, S2, S3, ....
(b) Solve the recurrence relation obtained in part (a).
2. (a)Find the order of a 9-regular graph with size 63.
(b) Let G be a graph of order 14 and size 25. If each vertex in G is of degree 3 or 5, then find the number of vertices of degree 5 in G.
3. (a)If the degree sequence of graph G is 4,3,3,2,2,2,0, then find the degree sequence of its complement graph G.
(b) If the size of graph G is 31 and the size of its complement G is 14 then find the order of G.