Let G be the graph on vertices V1, V2, ..., , V8 with the following adjacency matrix:1 0 0 0 0 0 11 0 1 0 0 0 010 1 0 0 1 0 0 10 0 0 0 0 1 1 00000010010001000000000000000101 1 1 0000Sketch all the graphs (up to isomorphism) on four vertices that are isomorphicto an induced subgraph of G (identifying a suitable induced subgraph in eachcase).

Step 1: Step 2:Step 3: Step 4: Step 5:Step 6:Step 7:

Answered: Let G be the graph on vertices V1, V2,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the relation R = {(a,b), (b, b), (b, c), (c, b), (c, c), (d, a), (d, c), (d, d)} on {a, b, c, d}. (a) Draw the digraph for R. (b) Write the adjacency matrix for R with respect to vertices in alphabetical order. (c) Draw the digraph for R o R.
5. Let G = (V, E) be a graph with vertex-set V = {1,2,3,4} and edge-set E = {(1, 2), (3, 2), (4, 3), (1, 4), (2,4)}. (a) Draw the graph. Find (b) maximal degree, i.e. A(G), (c) minimal degree, i.e. 8(G), (d) the size of biggest clique, i.e. w(G), (e) the size of biggest independent set, i.e. a(G), ter (f) the minimal number of colours needed to color the graph, i.e. x(G).
5. Let G₁ = (V₁, E₁1) be the following graph. We will show that it is not planar in three ways. E D F H G B (a) Find a subgraph that is isomorphic to a subdivision of either K5 or K3,3. Be sure to label the vertices! (b) Assume on the contrary that G is planar. Find V₁ and E₁, and use only these to explain that G is not planar. (c) Assume on the contrary that G is planar. Use Euler's Formula to find the number of faces and explain that G is not planar (hint: think about how we showed K is not planar)
20. Determine whether the graphs G and H in Figure 12.76 are isomorphic. G: 21 U3 22 Us U5 27 U6 ug H: V4 V2 V6 V1 V8 Figure 12.76: The graphs in Exercise 20 V3 07 V5
1. (a) Find the adjacency matrix of the following graph: (c) Draw 5 5 5 5 5S V3. VA V3 V2 U1 (b) Find the incidence matrix of the graph with vertex set {1, 22, 23, 24} and edge set {1x2, 14, 223, 234, 24}. the graph whose incidence matrix is: V6 V5 1 1 1 0 00000 V2 10 0110000 0001 0 1 100 0000 1 1 010 0 1 0 0 0 V6 0 0 1 0 0 0 0 1 1 0 1 0 1
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part 1 2 e graph theory
1. Let G be a graph with 7 vertices whose weight matrix is the following. Determine the Cover Tree

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