Explanation Given: The given network is: Procedure used: A path visit each vertex exactly once and end at the original vertex. Such a path is called a Hamiltonian cycle. A path begins at some vertex travel on each edge exactly once and then return to the starting vertex such a path is called an Euler circuit. Calculation: Consider the given network: From the definition of Hamiltonian cycle and Euler circuit: Hamiltonian = Euler circuit Euler circuit ≠ Hamiltonian Checking the Euler circuit is more easy than Hamiltonian. Draw the table for each vertex: vertex Edge passes through vertex Degree of vertex A AB, AF 2 B BA, BC 2 C CG, CD 2 D DC, DE 2 E DE, EF 2 F FG, FH 2 G GC, GF 2 H HF, HC 2 Degree of each vertex is degree 2, which is even. Therefore, the circuit is Euler circuit. We cannot conclude that whether Hamiltonian cycles exist or not. The possible paths are: Starting point Possible path

13th Edition

ISBN: 9781305855588

Author: SMITH

Publisher: CENGAGE CO

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Chapter 9.1, Problem 28PS

To determine

The Hamiltonian cycles for the given network.

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Chapter 9.1, Problem 27PS

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Chapter 9 Solutions

EBK NATURE OF MATHEMATICS

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