Define the following term related to graph theory
I. Tree & co-tree
II. Planer graph & non planer graph
III. Link & twig
Draw the graph corresponding to the following matrix and find
the no. of all possible tree.
discrete math a. Consider the following rooted tree: 7 10 11 12 i. What is the root? (1 marks) ii. What is the height of the tree? (1 marks) iii. What are the children of the vertex 3? (1 marks) a. Draw the directed graph corresponding to the adjacency matrix (2 marks) [1 0 0 ON 1 2 1 b. Using the adjacency matrix in (a) only, determine the number of walks of length 3 from each vertex to each...
(b) Given the following tree (graph) as shown in Figure 2: Diberi pepohon (graf) seperti yang ditunjukkan dalam Rajah 2: Figure 2 Rajah 2 (i) Find the pre-order traversal of the tree. Cari penyusuran pepohon "pre-order". (8/100) (ii) Find the post-order traversal of the tree. Cari penyusuran pepohon "port-order". (8/100) (iii Using the ordering c, d, e, f, g, h, i, j, k, I, m, a, b, c and the depth-first search algorithm, find a spanning tree for the graph...
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
Show all work for full credit. PART A Graph Theorv). 01.a. Model the following problem into a graph coloring problem A local zoo wants to take visitors on animal feeding tours, and is considering the following tours: Tour 1 visits the monkeys, birds, and deer Tour 2 visits the elephants, deer and giraffes; Tour 3 visits the birds, reptiles and bears Tour 4 visits the kangaroos, monkeys and bears Tour 5 visits birds, kangaroos and pandas; Monday, Wednesday and Friday...
7.5 (i) Prove that, if G is a bipartite graph with an odd number of vertices, then G is non-Hamiltonian. (ii) Deduce that the graph in Fig. 7.7 is non-Hamiltonian. Fig. 7.7 (iii) Show that, if n is odd, it is not possible for a knight to visit all the squares of an n chessboard exactly once by knight's moves and return to its starting point.
3 seperate questions multiple choice Determine which of the following matrices are in RREF. ſi 0 0 27 i) 0 2 0 3 0 1 1 4 ſi 0 1 0] i) 0 1 1 0 0 0 0 1 [1 0 -1 2 ii) 0 1 07 0 o [1 0 0 2 iv) 0 1 0 1 0 0 1 0 0 0 1 iv only ii and iii ii and iv i and ii For the given...
(1) For the following system of ODES: (i) First, convert the system into a matrix equation, then, (ii) Find the eigenvalues, 11 and 12, then, (iii) Find the corresponding eigenvectors, x(1) and x(2), and finally, (iv) Give the general solution (in vector form), ygen, of the system. (Parts (i)-(iii) will be in your work) s y = -241 + 742 y2 = yı + 4y2 General Solution:
4. Draw a simple (non-directional) graph G based on the given sets V(G) and E(G). V(G) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11) E(G) = { <1-2>, <1-3>, <2-4>, <2-5>, <3-6>, <5-7>, <5-8>, <6-9>, <9-10>, <8-11>} What type of a graph is it? A. Binary tree B. Full binary tree C. Complete binary tree D. Perfect binary tree 5. Find the diameter of the graph G in problem 4.12 points) D(G) = 6. Write the...
B1) List the benefits of networking. B2) List the responsibilities of a network administrator. B3) What is a local area network? B4) Define the following terms: (i) Point to Point link (ii) Topology (iii) MAC B5) What is a wide area network? B6) List the advantages of a peer to peer network. B7) List the advantages of a client/server network. B8) List the disadvantages of a peer to peer network. B9) Briefly explain client program and server program.
Could you please just solve Question (i) A: Thanks 3. For each of the following matrices, a. Determine the characteristic polynomial corresponding to the matrix. b. Find the eigenvalues of the matrix. c. For each eigenvalue, determine the corresponding eigenspace as a span of vectors. d. Determine an eigenvector corresponding to each eigenvalue. e. Pick one eigenvalue of each matrix and the corresponding eigenvector chosen in part (d) and verify that they are indeed an eigenvalue and eigenvector of the...