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(b) A simple graph is a finite set V of vertices together with a set E ? P(V) of edges. An edge is a two-vertex set {u, v} that can be represented as a line from u to v. The degree of a vertex v is the number edges containing v. For example the diagram shows a simple graph with eight edges and six vertices with degrees ranging from 0 to 4. Prove that any simple graph with n ? 2 vertices has at least two vertices of equal degree.

Name: (b) A simple graph is a finite set V of vertices together with a set E ? P(V) of edges. An edge is a two-vertex set u, v that can be represented as a line from u to v. The degree of a vertex v is the number edges containing v. For example the diagram shows a simple graph with eight edges and six vertices with degrees ranging from 0 to 4. Prove that any simple graph with n ? 2 vertices has at least two vertices of equal degree.
Uploaded: 2022-07-25T11:10:48-08:00
Duration: 4 min 15 s
Channel: Adi S

          (b) A simple graph is a finite set V of vertices together with a set E ? P(V) of edges. An edge is a two-vertex set {u, v} that can be represented as a line from u to v. The degree of a vertex v is the number edges containing v. For example the diagram shows a simple graph with eight edges and six vertices with degrees ranging from 0 to 4. Prove that any simple graph with n ? 2 vertices has at least two vertices of equal degree.

(b) A simple graph is a finite set V of vertices together with a set E ? P(V) of edges. An edge is a two-vertex set u, v that can be represented as a line from u to v. The degree of a vertex v is the number edges containing v. For example the diagram shows a simple graph with eight edges and six vertices with degrees ranging from 0 to 4. Prove that any simple graph with n ? 2 vertices has at least two vertices of equal degree.

Added by Elizabeth H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/25/2022

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Step 1: Consider a finite, simple graph G with n vertices where n is greater than or equal to 2. Show more…

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A simple graph is a finite set V of vertices together with a set E of edges. An edge is a two-vertex set {u,v} that can be represented as a line from u to v. The degree of a vertex v is the number of edges containing v. For example, the diagram shows a simple graph with eight edges and six vertices with degrees ranging from 0 to 4. Prove that any simple graph with n ≥ 2 vertices has at least two vertices of equal degree.