Chapter 5, Problem 32E

In Exercises 29 through 34 choose from the following answers and provide a short explanation for your answer using Euler’s theorems.

1. the graph has an Euler circuit.

2. the graph has Euler path.

3. the graph has neither an Euler circuit nor an Euler path.

4. the graph may or may not have an Euler circuit.

5. the graph may or may not have an Euler path.

6. there is no such graph.

$\begin{array}{l}1.\underset{\_}{Fig.5-44\left(a\right)}\\ 2.\underset{\_}{Fig.5-44\left(b\right)}\end{array}$

3. A graph with six vertices of degrees 1, 2, 3, 4, 5, and 6, respectively.

$$ $Figure5-44$