(a) Specify that the sum of the degrees of all vertices of a graph is double the number of edges in the graph.
(b) Let G be a non directed graph with L2 edges. If G has 6 vertices every of degree 3 and the rest have degree less than 3, what is the minimum number of vertices G can have?
(c) Explain the truth value for each of the following statements:
(i) 4 + 3 = 6 AND 3 + 3 = 6
(ii) 5 + 3 = 8 OR 3 + 1 = 5
(d) Let f(n)= 5 f(n/ 2) + 3 and f(1) = 7. Find f(2k) where k is a positive integer. Also estimate f(n) if f is an increasing function.
(e) Show the sufficient conditions of Dirac and Ore for a graph to be Hamiltonian. Give an instance of a graph that does not satisfy Dirac's condition, but satisfies Ore's condition.
(f) Measure -25 + 75 using 2's complement.