To prove: x ( G ) = n yet G does not have K n as sub-graph. Let n ≥ 4 be a natural number. And G be the graph that consist of union of K n − 3 and a 5-cycle C , together with all possible edges between the vertices.

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Answer 1

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Chapter 13.2, Problem 13E

To determine

To prove: x(G)=n yet G does not have Kn as sub-graph. Let n≥4 be a natural number. And G be the graph that consist of union of Kn−3 and a 5-cycle C, together with all possible edges between the vertices.

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Let Vn be the set of connected graphs having n edges, vertex set [n], and exactly one cycle. Form a graph Gn whose vertex set is Vn. Include {gn, hn} as an edge of Gn if and only if gn and hn differ by two edges, i.e. you can obtain one from the other by moving a single edge. Tell us anything you can about the graph Gn. For example, (a) How many vertices does it have? (b) Is it regular (i.e. all vertices the same degree)? (c) Is it connected? (d) What is its diameter?

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Answer 2

Question

Chapter 13.2, Problem 13E

To determine

To prove: x(G)=n yet G does not have Kn as sub-graph. Let n≥4 be a natural number. And G be the graph that consist of union of Kn−3 and a 5-cycle C, together with all possible edges between the vertices.

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Answer 3

Question

Chapter 13.2, Problem 13E

To determine

To prove: x(G)=n yet G does not have Kn as sub-graph. Let n≥4 be a natural number. And G be the graph that consist of union of Kn−3 and a 5-cycle C, together with all possible edges between the vertices.

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Answer 4

Question

Chapter 13.2, Problem 13E

To determine

To prove: x(G)=n yet G does not have Kn as sub-graph. Let n≥4 be a natural number. And G be the graph that consist of union of Kn−3 and a 5-cycle C, together with all possible edges between the vertices.

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Answer 5

Chapter 13.2, Problem 13E

To determine

To prove: x(G)=n yet G does not have Kn as sub-graph. Let n≥4 be a natural number. And G be the graph that consist of union of Kn−3 and a 5-cycle C, together with all possible edges between the vertices.

Answer 6

Chapter 13.2, Problem 13E

To determine

To prove: x(G)=n yet G does not have Kn as sub-graph. Let n≥4 be a natural number. And G be the graph that consist of union of Kn−3 and a 5-cycle C, together with all possible edges between the vertices.

Answer 7

Chapter 13.2, Problem 13E

To determine

To prove: x(G)=n yet G does not have Kn as sub-graph. Let n≥4 be a natural number. And G be the graph that consist of union of Kn−3 and a 5-cycle C, together with all possible edges between the vertices.

Answer 8

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Answer 11

Ch. 13.1 - Prob. 1TFQ Ch. 13.1 - Prob. 2TFQ Ch. 13.1 - Prob. 3TFQ Ch. 13.1 - Prob. 4TFQ Ch. 13.1 - Prob. 5TFQ Ch. 13.1 - Prob. 6TFQ Ch. 13.1 - Prob. 7TFQ Ch. 13.1 - Prob. 8TFQ Ch. 13.1 - Prob. 9TFQ Ch. 13.1 - Prob. 10TFQ

To prove: x ( G ) = n yet G does not have K n as sub-graph. Let n ≥ 4 be a natural number. And G be the graph that consist of union of K n − 3 and a 5-cycle C , together with all possible edges between the vertices.

Solution Summary: The author explains that G does not contain K_n as a sub-graph.

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To prove: x(G)=n yet G does not have Kn as sub-graph. Let n≥4 be a natural number. And G be the graph that consist of union of Kn−3 and a 5-cycle C, together with all possible edges between the vertices.

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