Question

a graph is given to the right.
a. explain why the graph has at least one euler circuit
b. use trial and error or fleury’s algorithm to find one such circuit

a. choose the correct explanation below.
a. it has exactly two odd vertices.
b. it has no even vertices
c. it has no odd vertices
d. all graphs have at least one euler circuit.
b. write an euler circuit starting at a
(use a comma to separate vertices as needed )

Explanation:

For part a, according to Euler's theorem, a graph has an Euler circuit if and only if it is connected and has no odd - degree vertices.
For part b, we can use trial and error. Starting from vertex A, we traverse the edges in a way that we don't get stuck until we return to A.

Answer:

a. C. It has no odd vertices
b. A, D, B, A, C, B, E, C, A (There are other possible correct answers for part b as well)