List all the odd vertices of the graph. b) According to Euler’s Theorem, does the graph have an Eulerian circuit? How do you know? c) According to Euler’s Theorem, does the graph have an Eulerian path? How do you know? What is the difference between a Hamiltonian path and an Eulerian path? A person starting in Columbus must-visit Great Falls, Odessa, and Brownsville (although not necessarily in that order), and then return home to Columbus in one car trip. The road mileage between the cities is shown

a) List all the odd vertices of the graph.
b) According to Euler’s Theorem, does the graph have an Eulerian circuit? How
do you know?
c) According to Euler’s Theorem, does the graph have an Eulerian path? How
do you know?

What is the difference between a Hamiltonian path and an Eulerian path?

A person starting in Columbus must-visit Great Falls, Odessa, and
Brownsville (although not necessarily in that order), and then return home to
Columbus in one car trip. The road mileage between the cities is shown

1. Draw a weighted graph that represents this problem in the space below. Use the first letter of the city when labeling each vertex.
2. Find the weight (distance) of the Hamiltonian circuit formed using the nearest neighbor algorithm. Give the vertices in the circuit in the order they are visited in the circuit as well as the total weight (distance) of the circuit. Remember to include the unit of measure in your final answer.

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