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Chapter 14: Problem 5

In Exercises 5-6, draw two equivalent graphs for each description. The vertices are \(A, B, C\), and \(D\). The edges are \(A B, B C, B D\), \(C D\), and \(C C\).

Short Answer

Expert verified
Two equivalent graphs can be created by keeping the edges and vertices constant while rearranging the position of the vertices. They should have the same number of vertices and edges, equivalent connections, and similar loops to ensure equivalence.

Step by step solution

01

Drawing Graph 1

For the first graph, start by drawing four distinct points to represent the vertices \(A, B, C\), and \(D\). Then, draw lines to represent the edges. Combination \(A B\) means there is an edge between vertex \(A\) and vertex \(B\). So, connect the vertices accordingly. Remember, \(C C\) implies a loop on vertex \(C\).
02

Drawing Graph 2

For the second graph, change the positions of the vertices but maintain the arrangements of the edges. Changing the positions of vertices does not affect the connections or the graph's equivalence, as the graph represents the vertices' relationships and connections, not their locations.
03

Ensuring equivalency

Ensure that the two graphs are indeed equivalent. They should have the same number of vertices and edges, the same connections, and the same loops. The locations of vertices can vary, but their connections must remain the same to maintain equivalency.

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