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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.
How large would the sample need to be if we are to pick a 95% confidence level sample: (i) From a population of 70; (ii) From a population of 450; (iii) From a population of 1000;
Group visible design is an arrangement of the v mn treatments in b blocks such that: * Each block comprises k distinct treatments k5v; * Each treatment is replicated r number
Command-Line options Compression: C++: ./compress -f myfile.txt [-o myfile.hzip -s Java: sh compress.sh -f myfile.txt [-o myfile.hzip -s] Decompression:
Primary Model Below is a regression analysis without 17 outliers that have been removed Regression Analysis: wfood versus totexp, income, age, nk The regression equat
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
Partial least squares is an alternative to the multiple regressions which, in spite of using the original q explanatory variables directly, constructs the new set of k regressor v
#explanation of methods of collection of data..
Procedures for estimating the probability distributions without supposing any particular functional form. Constructing the histogram is perhaps the easiest example of such type of
methods of determining trend in time series?
Generalized poisson distribution: The probability distribution can be defined as follows: The distribution corresponds to the situation in which the values of the rand
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