Questions: Consider the following graph. (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. The top and bottom vertices have degree 4, and the left and right vertices have degree 3. The top and left vertices have degree 3, and the bottom and right vertices have degree 4. All vertices have degree 2. All vertices have degree 3. All vertices have degree 4. (d) Determine whether the graph is connected. Yes No

Consider the following graph. (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. The top and bottom vertices have degree 4, and the left and right vertices have degree 3. The top and left vertices have degree 3, and the bottom and right vertices have degree 4. All vertices have degree 2. All vertices have degree 3. All vertices have degree 4. (d) Determine whether the graph is connected. Yes No
Transcript text: Consider the following graph. (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. The top and bottom vertices have degree 4, and the left and right vertices have degree 3. The top and left vertices have degree 3, and the bottom and right vertices have degree 4. All vertices have degree 2. All vertices have degree 3. All vertices have degree 4. (d) Determine whether the graph is connected. Yes No
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Solution

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Solution Steps

Step 1: Count the edges.

Each line segment connecting two vertices represents an edge. There are 8 edges in the graph.

Step 2: Count the vertices.

Each dot represents a vertex. There are 4 vertices in the graph.

Step 3: Determine the degree of each vertex.

The degree of a vertex is the number of edges connected to it. The top vertex has 4 edges connected to it (degree 4). The bottom vertex also has 4 edges connected to it (degree 4). The left and right vertices each have 3 edges connected to them (degree 3).

Final Answer

(a) 8 (b) 4 (c) The top and bottom vertices have degree 4, and the left and right vertices have degree 3. (d) Yes

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