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 D_4,2 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.

Posted Date: 3/5/2013 7:01:23 AM | Location : United States

Ask an Expert

Related Discussions:- Construct the de bruijn digraph, Assignment Help, Ask Question on Construct the de bruijn digraph, Get Answer, Expert's Help, Construct the de bruijn digraph Discussions

Write discussion on Construct the de bruijn digraph
Your posts are moderated

Write your message here..

Related Questions

Ehrenberg''s equation, The equation linking the height and weight of the ch... The equation linking the height and weight of the children between the ages of 5 and 13 and given as follows   here w is the mean weight in kilograms and h the mean height in

Last observation carried forward, Last observation carried forward is a te... Last observation carried forward is a technique for replacing the observations of the patients who drop out of the clinical trial carried out over a time period. It consists of su

Incubation period, Incubation period is the time elapsing amongs the receip... Incubation period is the time elapsing amongs the receipt of infection and the appearance of the symptoms. The length of the incubation time period depends on the disease, ranging

Tree, Tree is the term from the branch of the mathematics which known as t... Tree is the term from the branch of the mathematics which known as the graph theory, used to describe any set of the straight-line segments joining the pairs of points in some pro

Functional data analysis, The analysis of data which are the functions obse... The analysis of data which are the functions observed continuously, for instance, functions of time. Basically a collection of statistical techniques or methods for answering quest

Latin square design, literature review of latin square design. literature review of latin square design.

Simplex method, Economic Interpretation of the Optimum Simplex solution Economic Interpretation of the Optimum Simplex solution

Dirichlet tessellation, A construction for events that happen in some plana... A construction for events that happen in some planar area a, consisting of the series of 'territories' each of which comprises of that part of a closer to the particular event xi t

Tests for heteroscedasticity, Lagrange Multiplier (LM) test The Null Hy... Lagrange Multiplier (LM) test The Null Hypothesis - H0: There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1:  There is heteroscedasticity i.e. β 1

Hypothesis testing and chi-square tests.., The results of a survey determin... The results of a survey determined whether the age of a driver 21 years and older has any effect on the number of motor vehicle accidents in which he/she is involved. Question 1: