3. Consider the following graphs G₁, G2, and G3G₁ is the graph with vertex set {1, 2, 3, 4, X5, X6, 7, 8},and edge set {1x2, X1X7, X1X8, X2X3, X3X4, X3 X5, X3X6, X3X7, X4X5, X5X6, X7X8}.• G₂ is the graph with vertex set (y₁, Y2, Y3, Y4, Y5, Y6, y7, ys} and adjacency matrix:Y1Y2Y3Y4Y50 1 0 1 1 1 1 010 1 00 0 0 001 0000 1 11 0 0 010001 0 0 1 0 1 0 01 0 01 0 10 10 0 00 0 0 0 10 0 1 0 0 0 1 02728Y6Y7Y8• G3 is the graph with vertex set {21, 22, 23, 24, 25, 26, 27, 28} and incidence matrix:2₁ 1 122232425261 0 0000 0 000 0 10 0 000 0001 011000000 0 0011 1 0 0 0 00 0 0 0 01 0 1 0 0 001 11 1 01 0 0 00 0 0 0 0 0 0 0 1 0 100000000011(a) Exactly two of the three graphs are ismorphic. Which two are they?(b) Provide an isomorphism between the two graphs you picked in part (a).

3. Consider the following graphs G₁, G2, and G3 G₁ is the graph with vertex set {1, 2, 3, 4, X5, X6, 7, 8}, and edge set {x1x2, X1X7, X1X8, X2X3, X3 X4, X3X5, X3X6, X3X7, X4 X5, X5 X6, X7X8}. • G₂ is the graph with vertex set (y₁, Y2, Y3, Y4, Y5, Y6, y7, ys} and adjacency matrix: 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 000 1 0 0 1 0 1 0 0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 • G3 is the graph with vertex set {21, 22, 23, 24, 25, 26, 27, 28} and incidence matrix: 1 1 0 0 1 0 0 0 0 0 27 28 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 2₁ 1 1 22 23 24 25 26 1 0 0000 0 00 00 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0000 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 00000000011 (a) Exactly two of the three graphs are ismorphic. Which two are they? (b) Provide an isomorphism between the two graphs you picked in part (a).

3. Consider the following graphs G₁, G2, and G3 G₁ is the graph with vertex set {1, 2, 3, 4, X5, X6, 7, 8}, and edge set {x1x2, X1X7, X1X8, X2X3, X3 X4, X3X5, X3X6, X3X7, X4 X5, X5 X6, X7X8}. • G₂ is the graph with vertex set (y₁, Y2, Y3, Y4, Y5, Y6, y7, ys} and adjacency matrix: 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 000 1 0 0 1 0 1 0 0 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8 • G3 is the graph with vertex set {21, 22, 23, 24, 25, 26, 27, 28} and incidence matrix: 1 1 0 0 1 0 0 0 0 0 27 28 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 2₁ 1 1 22 23 24 25 26 1 0 0000 0 00 00 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0000 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 00000000011 (a) Exactly two of the three graphs are ismorphic. Which two are they? (b) Provide an isomorphism between the two graphs you picked in part (a).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Which of the following is the edge set of the graph (G) below? B A E D E(G) = {A, B, C, D, E) E(G) = {AB, BC, CE, AC, AE, AD, BE, DE, CC} E(G) = {AB, BC, CE, AC, AE, AD, CD, BE, DE, CC) E(G) = {AB, BC, CE, AC, AE, AD, BE, DE} Referring to the graph (G) below, determine the degree of vertex C. B A6 E 2 5 D
9. (a) Draw a simple graph (no loops or multiple edges) with vertex degrees 2,3,3,3,4,4,4,5. (b) How many edges does its complement have? Explain.
Construct a graph with vertices P, Q, R, S, T, U whose degrees are 4, 3, 2, 3, 3, 1 What is the edge set?
Explain thoroughly!!
2. Let G be a connected (simple) planar graph where the number of vertices = 8. What can be said about the possible number of edges?
Give an example of a non-planar graph that is not homeomorphic to K5or K3,3.
Which of these graphs have the property that the removal of any vertex and all edges incident with that vertex produces a planar graph? K7 K5 K4,4 K3,4
Construct a simple graph that is a forest with vertices O, P, Q, R, S, T, U, V such that the degree of U is 2 and there are 3 components. What is the edge set? You have attempted this problem ti
Consider the following two graphs G1 = {{a,b, c, d, e, f}, {ab, a f, ae, bc, bf, be, cd, cf, df, ef}}, and G2 = {{v1, v2, v3, v4, V5, V6}, {v1v2, v1V3, V1V4, V1 V5, V2V3, V2V6, V3V4, V3V5, V3 V6, V4V5}}, %3D (a) is the function b c d f a e U5 v2 V4 V3 a graph isomorphism? (b) can you construct a bijection of vertices that is not an isomorphism? explain. (c) provide a drawing that represents this isomorphism class.
Consider the graph G with • V(G) = {2,3,6} • e(G) = {a, b, c, d, e, f, g} •E(G) = {(a, [2,2]), (b, [3,3]), (c, [6,6]), (d, [2,6]), (e, [6,2]), (f, [3,6]), (g, [6,3])} Using edge connectivity, we can define the relation R = {(2, 2), (3, 3), (6, 6), (2, 6), (6, 2), (3, 6), (6,3)} Which of the following statements are true? [More than one statement may be true.] R is reflexive. R is symmetric. R is transitive. R is antisymmetric.
if it is known that the graph has no direction G with the notation G = (V, E); V = (1, 2, 3, 4, 5, 6); E = (12, 14, 15, 23, 25, 26, 34, 36, 45, 46, 56) and there is a connected graph G' which is a subgraph of G which also has many vertices is 6 (| G'.V | = | GV |) and the minimal number of edges. a.how many G'(spanning tree)?