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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.
If each interior angle of a regular polygon has a calculated as of 144 degrees, Determine the numbers of sides does it have? a. 8 b. 9 c. 10 d. 11 c. The measur
Bikes are on sale for 30% off the original price. What percent of the original price will the customer pay if he gets the bike at the sale price? The original price of the bike
explain under a reflection the image is laterally inverted.
a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain t
Squeeze Theorem (Sandwich Theorem and the Pinching Theorem) Assume that for all x on [a, b] (except possibly at x = c ) we have, f ( x )≤ h (
Explain Simplifying Rational Expressions ? A rational expression, or algebraic fraction, is an expression in which you have a polynomial divided by a polynomial. Sometimes it
modular arithematic
Rectilinear Distance (Total Travel Distance per Day Using Rectilinear Distance): It can be computed through using following formula: d(X, Pi) = |x - ai| + |y - bi| (Source: T
Let E; F be 2 points in the plane, EF has length 1, and let N be a continuous curve from E to F. A chord of N is a straight line joining 2 points on N. Prove if 0 and N has no cho
what is 36 percent as a fraction in simplest form
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