In the following, all graphs are simple. Check all that apply.x(G) is the number of colors used in greedy coloring.If G is 4-colorable, then its chromatic number if 4.If G and H are isomorphic, then x(G) = x(H).If G contains a subgraph isomorphic to X4, then its chromatic number is at least 4.

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Answered: In the following, all graphs are…

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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Show that the pair of graphs are not isomorphic by showing that there is a property that is preserved under isomorphism which one graph has and the other does not. Figure 5: Two undirected graphs. The ﬁrst graph has 5 vertices, in the form of a regular pentagon. From the top vertex, moving clockwise, the vertices are labeled: 1, 2, 3, 4, and 5. Undirected edges, line segments, are between the following vertices: 1 and 2; 2 and 3; 3 and 4; 4 and 5; and 5 and 1. The second graph has 4 vertices, a through d. Vertices d and c are horizontally inline, where vertex d is to the left of vertex c. Vertex a is above and between vertices d and c. vertex b is to the right and below vertex a, but above the other two vertices. Undirected edges, line segments, are between the following vertices: a and b; b and c; a and d; d and c; d and b.
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In the following, all graphs are simple. Check all that apply. x(G) is the number of colors used in greedy coloring. If G is 4-colorable, then its chromatic number if 4. If G and H are isomorphic, then x(G) = x(H). If G contains a subgraph isomorphic to X4, then its chromatic number is at least 4.