Chapter 5, Problem 30E

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

A. the graph has an Euler circuit.

B. the graph has Euler path.

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

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

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

F. there is no such graph.

a. Fig. 5-42(a)

b. Fig. 5-42(b)

c. A connected graph with eight vertices: four vertices of degree 2 and four vertices of degree 3.

d. A graph with eight vertices: four vertices of degree 4 and four vertices of degree 3.

e. A connected graph with nine vertices of degree 3.