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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.
The growth in bad debt expense for Johnston office supply Company over this time period.If this rate continues,estimate the percentage increase in bad debts for 1997,relative to 19
Respondent-driven sampling (RDS ): The form of snowball sampling which starts with the recruitment of the small number of people in the target population to serve as the seeds. Aft
i have an assignment for experimental design which is must done by SAS program can you help me also i need to hand in the assignment till thursday shall i send it for you ?
Q1: The growth in bad debt expense for Aptara Pvt. Ltd. Company over the last 20 years is as follows. 1997 0.11 1998 0.09 1999 0.08 2000 0.08 2001 0.1 2002 0.11 2003 0.12 2004 0.1
Cellular proliferation models : Models are used to describe the growth of the cell populations. One of the example is the deterministic model where N(t) is the number of cel
#q A paper mill products two grade of paper viz., X & Y. Because of raw material restriction, it cannot produce more than 400 tons of grade X paper & 300 tons of grade Y paper in a
The graphical method for studying the behavior of the seasonal time series. In such a plot, the January values of seasonal component are graphed for the upcoming years, then the
The plot of the number of cases of the disease against the time period. A large and sudden increase corresponds to an epidemic. The example of this is shown in the figure drawn bel
Common cause failures (CCF): Simultaneous failures of the number of components due to a same reason. A reason can be external to the components, or it can be the single failure wh
Response surface methodology (RSM): The collection of the statistical and mathematical methods useful for improving, developing, and optimizing processes with significant applicat
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