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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.
a sequence of numbers consist of six 6''s seven 7''s eight 8''s nine 9''s ten 10''s what is the arithmetic mean?
Chains of infection : The description of the course of infection among the group of individuals. The susceptibles infected by the direct contact with the introductory cases are sai
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Hello-goodbye effect : The phenomenon initially described in psychotherapy research, but one which might arise whenever a subject is assessed on two occasions, with some interventi
An oil company thinks that there is a 60% chance that there is oil in the land they own. Before drilling they run a soil test. When there is oil in the ground, the soil test comes
what is the combine standard deviation height from the follwing
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
Chain-binomial models : Models arising in mathematical theory of the quite infectious diseases, which postulate that at any stage in the epidemic there are a certain number of the
Banach's match-box problem : The person carries two boxes of matches, one in his left and one in his right pocket. At first they comprise N number of matches each. When the person
Treatment allocation ratio is the ratio of the number of subjects allocated to the two treatments in a clinical trial. The equal allocation is most usual in practice, but it might
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