Chapter 14, Problem 1RE

Explain why the two figures show equivalent graphs. Then draw a third equivalent graph.

To determine

The reason that the two-provided graphs are equivalent and then draw a third equivalent graph.

Answer to Problem 1RE

Solution:

Both the graphs are equivalent and third equivalent graph is;

Explanation of Solution

Given:

Consider the provided graphs;

Explanation:

In both figures, the vertices are A, B, C, D and E. Both graphs have an edge that connects vertex A to vertex B (edge AB or BA ), an edge that connects vertex B to vertex C (edge BC or CB ), an edge that connects vertex A to vertex E (edge AE or EA ), an edge that connects vertex A to vertex C (edge AC or CA ) and an edge that connects vertex A to vertex D (edge AD or DA ). Because the two graphs have the same number of vertices connected to each other in the same way, they are equivalent.

Third equivalent graph is;