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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.
Regression to the mean is the procedure first noted by Sir Francis Galton that 'each peculiarity in man is shared by his kinsmen, but on average to the less degree.' Hence the ten
HOW TO CONSTRUCT A BIVARIATE FREQUENCY DISTRIBUTION
hello I have a dataset including both categorical & numerical variable for market segmentation.how can i cluster them via k-means in matlab? thank you
Ascertainment bias : A feasible form of bias, particularly in the retrospective studies, which arises from the relationship between the exposure to the risk factor and the probabil
MEANING ,IMPORTANCE AND RELEAVANCE OF SCATTER DIAGRAM
Ordinal variable is a measurement which allows a sample of the individuals to be ranked with respect to some characteristic but where differences at different points of the scale
Incidental parameter problem is a problem which sometimes occurs when the number of parameters increases in the tandem with the number of observations. For instance, models for pa
Histogram is the graphical representation of the set of observations in which class frequencies are represented by the regions of rectangles centred on the class interval. If the f
Genetic algorithms: The optimization events motivated by the biological analogies. The prime idea is to try to mimic the 'survival of the fittest' rule of the genetic mutation in
It is the multivariate normal random vector which satisfies certain conditional independence suppositions. This can be viewed as a model framework which contains a wide range of st
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