Given a graph with this adjacency matrix: Note: this matrix will be used for this question and the questions after that. V_1 v_2 v 3 V_ 4 v_5 v_6 1. 0 0 1 1 1 1 1 1 1 How many paths of length 1 are there from vertex v5 to vertex v_3 1. 1. 1, 5. 6.
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- 1. determine the type of graph of the figure 2.solve for the adjacency matrix of the givenThe adjacency matrix of the following graph isConsider the adjacency matrix for a graph that is shown below. Answer the following questions by examining the matrix and its powers only, not by drawing the graph. Show your work in a way that makes your reasoning clear. (a) How many walks of length 2 are there from v1 to v3? (b) How many walks of length 3 are there from v1 to v2?
- Find the adjacency matrix of the intersection of W4 and K5. What is the degree of vertexes in W4 K5.Use powers of adjacency matrices to determine the number of paths of th e specified length between the given vertices length 4, v2 and v2Given the following adjacency matrix: v1 v2 v3 v4 M = ⌈ 1 1 2 0 ⌉ v1 | 0 0 1 0 | v2 | 0 0 1 1 | v3 ⌊ 1 2 0 1 ⌋ v4 A. Determine the corresponding graph. 2. Determine the matrix that will give the number of all paths with length two (i.e., compute M2; you must show ALL work!).
- Use powers of adjacency matrices to determine the number ofpaths of the specified length between the given vertices. length 2, v2 to v3The following is an adjacency matrix for a graph: ? = [0 1 1 01 0 2 11 2 0 10 1 1 1]Answer the following questions by examining the matrix and its powers only, not bydrawing the graph:a) How many walks of length 2 are there from v2 to v3?b) How many walks of length 2 are there from v3 to v4?c) How many walks of length 3 are there from v1 to v4?d) How many walks of length 3 are there from v2 to v3?When a graph is mapped into a matrix this is called a(n) ___________ matrix
- Find a square matrix P which can be used as a premultiplier of a 5-by-5 matrix A to effect the following changes in A: row 1 to row 2, row 2 to row 1, row 3 to row 4, row 4 to row 5, row 5 to row 3Which of the following are true for the adjacency matrix of the attached graph? 1. ||A||F = 4 2. A[1,.... ,1]T gives the vector of all out-degrees (number of edges out from a vertex) 3. ||A|| infiniti = 3 4. A is symmetricLet M be the incidence matrix and A the adjacency matrix of a graph G.(a) Show that every column sum of M is 2.(b) What are the column sums of A?