This complete network has three different Hamiltonian cycles. Write down the three cycles.

Given graph is A Hamiltonian cycle is a path which travels through every vertex exactly once and returns to its starting vertex. If the order of two hamiltonian cycles are same but different starting vertex, then they are same cycles. For given graph, Three different Hamiltonian cycles are A - B - H - G - A A - H - G - B - A A - H - B - G - A

This complete network has three different Hamiltonian cycles. Find the weight of each cycle.

Given graph is A Hamiltonian cycle is a path which travels through every vertex exactly once and returns to its starting vertex. If the order of two hamiltonian cycles are same but different starting vertex, then they are same cycles. For given graph, Three different Hamiltonian cycles are 1) A - B - H - G - A Weight of cycle = 19 + 11 + 23 + 27 = 80 2) A - H - G - B - A Weight of cycle = 17 + 23 + 18 + 19 = 77 3) A - H - B - G - A Weight of cycle = 17 + 11 + 18 + 27 = 73

This complete network has three different Hamiltonian cycles. Hence find the shortest Hamiltonian cycle for this network.

Given graph is A Hamiltonian cycle is a path which travels through every vertex exactly once and returns to its starting vertex. If the order of two hamiltonian cycles are same but different starting vertex, then they are same cycles. For given graph, Three different Hamiltonian cycles are 1) A - B - H - G - A Weight of cycle = 19 + 11 + 23 + 27 = 80 2) A - H - G - B - A Weight of cycle = 17 + 23 + 18 + 19 = 77 3) A - H - B - G - A Weight of cycle = 17 + 11 + 18 + 27 = 73 So, the shortest Hamiltonian cycle for this network is the one with lowest weight that is A - H - B - G - A

E M B I B E

Extended MYP Mathematics A Concept based approach Years 4 & 5>Is Something Networking?>Chapter 18 - Graph Theory: Networks>Exploration 5

Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 12: Exploration 5

Author:Rose Harrison, Clara Huizink, Aidan Sproat Clements & Marlene Torres Skoumal

Rose Harrison Mathematics Solutions for Exercise - Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 12: Exploration 5

Attempt the free practice questions from Exercise 12: Exploration 5 with hints and solutions to strengthen your understanding. Extended MYP Mathematics A Concept based approach Years 4 & 5 solutions are prepared by Experienced Embibe Experts.