First we create a matrix from a graph since the problem asks to be solved using graph theory.
Let be a graph on
We create a matrix from as follows:
If there exists any edge between two vertices we write otherwise we put it
Thus we get a matrix which we call .
Now assume that there exists no such column of such that deleting will result in at least two rows being identical
which in turn implies that if we delete any column of then at least two rows will become same.
Thus it implies that the two rows differed only in the entries of that column.
But note that thuis is true for any column of A.
But in the matrix A we only have two distinct elements .
Thus it is absurd because all the rows are given to be non-identical in .
Thus there exists at least one column whose deletion results in a array with no two rows same.
Please write legibly Bonus problem: Use graph theory to solve the following problem. Let A be...
Using python; We wish to use graph theory in order to solve the following problem. A company should carry dierent chemical products P1, P2, : : :, Pk from the factory to a city. For security reasons, some products should not be carried in the same truck: 8i; 0 < i < k; Pi is not compatible with Pi+1. Moreover Pk is not compatible with P1. 1) Write a comment: how can we state an undirected graph that visually represents...
Can someone please show all your work and steps for this problem? Please write really legibly and make it easier for me to understand... The answer is ALREADY there so PLEASE make sure to double check your work and make sure your answer matches. Thanks in advance!
Can someone please show all your work and steps for this problem? Please write really legibly and make it easier for me to understand... The answer is ALREADY there so PLEASE make sure to double check your work and make sure your answer matches. Thanks in advance!
Problem 5. (20 pts) Let r,n N be two natural numbers with r < n. An r x n matrix M consisting of r rows and n columns is said to be a Latin rectangle of size (r, n), if all the entries My belong to the set {1,2,3,..., n), for 1Si<T, 1Sj<T, and the same number does not appear twice in any row or in any column. By defini- tion, a Latin square is a Latin rectangle of size...
Let M be an n x n matrix with each entry equal to either 0 or 1. Let mij denote the entry in row i and column j. A diagonal entry is one of the form mii for some i. Swapping rows i and j of the matrix M denotes the following action: we swap the values mik and mjk for k = 1,2, ... , n. Swapping two columns is defined analogously. We say that M is rearrangeable if...
Please help with this C++ problem using Array Use a one-dimensional array to solve the following problem. Read in 20 numbers, each of which is between 10 and 100. As each number is read validate it and store it in the array. After reading all the values, display only the unique values that the user entered. Make sure you account for the worst case scenario in which all 20 numbers are different. Use the smallest possible array to solve this...
cope the code please thanks Write a MATLAB code to obtain the following. Keep your code commented whenever required. Copy your source code and command widow outcomes and screen shots of any plots in your solution. Generate a matrix "A" as follow. A= 16 6 8 2 10 18 12 14 4 I. II. Divide the matrix A by 2 and store the result in a matrix B. Combine matrices A & B to obtain the following matrix C. Also...
Prove the following lemma. Let B be an n ✕ n matrix and let E be an n ✕ n elementary matrix. Then det(EB) = det(E) det(B) 1. Write the proof and submit as a free response. (Submit a file with a maximum size of 1 MB.) 2. Which of the following could begin a direct proof of the statement? If E interchanges two rows, then det(E) = 1 by Theorem 4.4. Also, EB is the same as B but...
write a Matlab program ( solve the three questions). please use array and create your own function to check primality Question 1 : [10 points) Write a MATLAB program that will store all the first 1000 prime numbers in an array variable named arr_of_primes. Please note that a prime number is a positive integer that is bigger than or equal to 2 which is divisible only by 1 and itself. Examples of the first 8 primes are: 2, 3, 5,...
refer to the question using c++. if you could not do the bonus part no problem you don't have too , but if you can so please do it and let me know Create an unweighted undirected Graph Class using an Adjacency Matrix with the following functions 1. Graph(int numofV) 3. int noOfOutgoingEdges(int vertex); 4. int noOflncomingEdges (int vertex) 5. void print) You may use vectors/2D dynamic arrays to implement the matrix. Bonus (20) 6. void DFS(); Depth First Search...