Explanation Given: The following figure shows the given diagram. Approach: According to the Euler theorem if there are exactly two odd vertices in a connected graph then there will be at least one Euler trail, which is also an Euler Circuit. A connected graph with exactly two odd vertices and any number of even vertices has at least one Euler Trail... To determine b) The Euler trail or Euler circuit in the graph if the graph has it. Otherwise, Eulerize the graph, if possible.

8th Edition

ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Chapter 9.CR, Problem 16CR

To determine

a)

Whether the graph has an Euler trail or an Euler circuit.

To determine

b)

The Euler trail or Euler circuit in the graph if the graph has it. Otherwise, Eulerize the graph, if possible.

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Chapter 9.CR, Problem 15CR

Chapter 9.CR, Problem 17CR

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a) Whether the graph has an Euler trail or an Euler circuit.

Solution Summary: The author explains that an Eulerian trail is a trail in the graph which visits every edge exactly once, and an E-circuit which starts and ends on the same vertex.