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(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.
In a class, all pupils take Mathematics (M), 18 take Chemistry (C), 17 take Biology (B) and 24 take Physics (P) of those taking 3 subjects only, 5 take Physics and Chemistry, 7 ta
whats 2x2
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I need help on radical notation for a homework assignment I''m really confused on it. Can I get help?
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Consider a database whose universe is a finite set of vertices V and whose unique relation .E is binary and encodes the edges of an undirected (resp., directed) graph G: (V, E). Ea
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
PLAY AND LEARN : Children can learn many basic mathematical concepts through games. They enjoy Mathematical concepts can be playing within familiar contexts. Their games also gen
Find the distance between the points (b + c, c + a) and (c + a, a + b) . Ans : Use distance formula
I have 6 cups of patatos that I have to share with 13 friends write that as the nearest hundredth
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