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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.
Each of the series 3+5+7+..... and 4+7+10.......... is continued to 100 terms find how many terms are identical. Ans) 48 terms would be common to both the series... first take co
Inverse Cosine : Now see at inverse cosine. Following is the definition for the inverse cosine. y = cos -1 x ⇔ cos y = x for
a) A palindrome is a word that reads the similar whether read from right to left or from the left to right, the word ROTOR, for example. Let be the number of words of length n,
The population of the village is 5000. If in a year, the number of males were to increase by 5% and that of a female by 3% annually, the population would grow to 5202 at the end o
Two circles touch each other externally: Given: Two circles with respective centres C1 and C2 touch each other externaly at the point P. T is any point on the common tangent
Ask question #Minimum 100 words accepted what is a ratio
A poll tilts towards the sun at an 8 o angle from the vertical at it casta 22-ft shadow. The angle of elevation from the shadow to the top of the pole is 43 o . How tall is th
2. Suppose a file of 35,000 characters is to be sent over a line at 55,000bps. 1. Calculate the overhead in bits and time using asynchronous transmission. Assume 1 start bit
Q. How to calculate Percentiles? Ans. In a large group of standardized test scores we expect the scores to approximate a normal curve. If all scores are translated to z-s
Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve
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