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A directed graph is simple if each ordered pair of vertices is the head and tail of at most one edge; one loop may be present at each vertex. For each n ≥ 1, prove or disprove the following statement. Every simple directed graph with n vertices has two vertices with the same outdegree or two vertices with the same indegree.
(a) How many words of length 2 are there over the alphabet A = { 0; 1; 2; 3}?
(b) Construct the de Bruijn digraph D4,2 and use this digraph to nd an appropriate de Bruijn sequence.
(c) For b = 4 and n = 2, how many de Bruijn sequences can be formed?
Suppose [S, T] and [X, Y ] are two minimal cuts in a network N. Prove that both [S [X U T ∩ Y ] and [S ∩ X, T U Y ] are also minimal cuts in N.
L'Abbe ´ plot is often used in the meta-analysis of the clinical trials where the result is the binary response of it. The event risk (number of events/number of the patients in a
Average age at death : A ?awed statistic summarizing expectancy of the life and other aspects of the mortality. For instance, a study comparing average age at the death for male sy
Ask questT-TEST? ion #Minimum 100 words accepted#
The diagnostic tools or devices used to approach the closeness to the linearity of the non-linear model. They calculate the deviation of so-called expectation surface from the plan
how to resolve sequencing problem if jobs 6 given and 4 machines given. how to apply johnson rule for making to machines under this conditions. please give solution as soon as poss
It is the technique used in the clinical trials when it is possible to make an acceptable place before an active treatment but not to make the two active treatments identical. In t
what is pdf,mean & variance for multimodal distribution?
replacement problem
The biggest and smallest variate values among the sample of observations. Significant in various regions, for instance flood levels of the river, speed of wind and snowfall.
A manufacturing company has two factories F 1 and F 2 producing a certain commodity that is required at three retail outlets M 1 , M 2 and M 3 . Once produced, the commodity is
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