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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5, Problem 1RE

Textbook Problem

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(a) determine the number of edges in the graph, (b) find the number of vertices in the graph, (c) list the degree of each vertex, and (d) determine whether the graph is connected.

To determine

**(a)**

The edges in the graph.

The number of edges in the given graph is 8.

**Given:**

**Calculation:**

The number of available edges in the given graph is 8.

**Conclusion:**

The number of edges in the given graph is 8.

To determine

**(b)**

The vertices present in the graph..

The vertices present in the given graph are 4.

**Given:**

**Calculation:**

The available number of vertices in the given is 4.

**Conclusion:**

The vertices present in the given graph is 4.

To determine

**(c)**

**To list:**

The degree of every individual vertex.

Vertex A has degree 4, vertex B has degree 4, vertex C has degree 4 and vertex D has degree 4.

**Given:**

**Calculation:**

Vertex A has degree 4, vertex B has degree 4, vertex C has degree 4 and vertex D has degree 4.

**Conclusion:**

Vertex A has degree 4, vertex B has degree 4, vertex C has degree 4 and vertex D has degree 4.

To determine

**(d)**

**To say:**

Whether the graph is connected are or not.

The graph is connected since each vertex are connected to one another.

**Given:**

**Calculation:**

As each vertex are connected to one another the graph is said to be connected.

**Conclusion:**

As each vertex are connected to one another the graph is said to be connected.

Mathematical Excursions (MindTap Course List)

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