Let G be the graph on vertices V1, V2, ..., U8 with the following adjacency matrix:0100 0001 0 1 000010100 100 100000110001000000 0 0 1 0000000 100001 1 100 000Sketch all the graphs (up to isomorphism) on four vertices that are isomorphicto an induced subgraph of G (identifying a suitable induced subgraph in eachcase).Sketch all the graphs (up to isomorphism) on four vertices that are not iso-morphic to an induced subgraph of G.Find a graph on four vertices that is isomorphic to a subgraph, but not to aninduced subgraph, of G. Explain your answer.

soluyion:The given adjacency matrix is as follows: 0 1 0 0 0 0 0 11 0 1 0 0 0 0 10 1 0 1 0 0 0 00 0…

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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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).
b,c,d
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