Find a recurrence relation for the number of bit strings of length 7 that contain a pair of consecutive 0s.

1.      Suppose that a connected planar graph has six vertices, each of degree four. Into how many regions is the plane divided by a planar representation of this graph?

1.      

1.      Closed form for the generating function a_n=2 for n=3,4,5,…

1.      For which values of m and n does the complete bipartite graph K_m,n  have a Hamilton circuit?

1.      How much storage is needed to represent a simple graph with n vertices and m edges using adjacency list

1.      How many non isomorphic simple graphs are there with four vertices

1.      The number of edges in Q₅ is

1.      How many subgraphs with at least one vertex does W₃ have?

1.      If G(x) is the generating function for the sequence {a_k} then what is the generating function for a_o, a₀+a₁, a₀+a₁+a₂, …….

1.      Find f(n) when n=4^k, where f satisfies the recurrence relation f(n) = 5f(n/4)+6n with f(1) =1