Mathematics of GraphsYou are having a Christmas vacation in Europe. You want to visit these four different beautiful placesand return to your hotel while minimizing your total travel time. Represent the estimated travel timebetween places using a weighted graph. Moreover, use the greedy algorithm and the edge-pickingalgorithm to find a possible route starting and ending at your hotel. The travel time is in minutes.HomePlace APlace BPlace CPlace DHome30271812Place APlace BPlace C3042223727421831182218Place D12373125

The time taken to visit each place from home is given as follows: Home Place A Place B Place C…

Answered: You are having a Christmas vacation in…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter6: Ratio, Proportion, And Probability

Section6.8: The Multiplication Principle

Problem 16E

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Route Planning Brian needs to visit the pet store, the shopping mall, the local farmersmarket, and the pharmacy. His estimated driving times (in minutes) between thelocations are given in the table below. Use the greedy algorithm and the edge-pickingalgorithm to find two possible routes, starting and ending at home, that will helpBrian minimize his total travel time
7. ***PIcture*** Apply the sorted edges algorithm to the graph above. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDEA =_____________
[2B] The given table below shows the 5 different places that you would like to visit on a particular day. The table below shows the estimated distance (in kilometers per hour) it takes you to travel from one place to another. If you will visit each of these places exactly once, determine the shortest time possible it would take you to do using the Edge-Picking Algorithm. Examples already provided in the photos below. Home Hospital Mall Esplanade Pet Shop Market Home --- 2.00 km/h 4.00 km/h 3.53 km/h 6.00 km/h 20.00 km/h Hospital 2.00 km/h --- 3.53 km/h 3.00 km/h 2.40 km/h 2.61 km/h Mall 4.00 km/h 3.53 km/h --- 30.00 km/h 2.40 km/h 3.33 km/h Esplanade 3.53 km/h 3.00 km/h 30.00 km/h --- 2.22 km/h 3.00 km/h Pet Shop 6.00 km/h 2.40 km/h 2.40 km/h 2.22 km/h --- 8.57 km/h Market 20.00 km/h 2.61 km/h 3.33 km/h 3.00 km/h 8.57 km/h ---
“District mathematics” Find the length of a shortest path between a and z in the given weighted graph by using Dijiksta algorithm.
The table below shows the cost of direct train travel between various cities. QUESTION A: Draw a weighted graph that represents the train fares. Use the Edge-Picking Algorithm to find a route that begins in Angora, visits each city, and returns to Angora. What is the total cost of this route?
[2B] (Please type and draw your answers digitally).The given table below (1st picture) shows the 5 different places that you would like to visit on a particular day. The table below shows the estimated distance (in kilometers per hour) it takes you to travel from one place to another. If you will visit each of these places exactly once, determine the shortest time possible it would take you to do using the Edge-Picking Algorithm. Example (2nd photo) already provided in the photos below.
Apply the sorted edges algorithm to the graph above. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDEFA
[P8] (Use Djikstra’s Algorithm - Query ) What is the shortest path from A to G?
6. ***Picture*** Apply the repeated nearest neighbor algorithm to the graph above. Starting at which vertex or vertices produces the circuit of lowest cost? (there may be more than one answer) A BC D E
Applied combinatorics 14) A graph G is called maximal planar if G is planar but the addition of anotheredge between two nonadjacent vertices will make the graph nonplanar.(a) Show that every region of a connected, maximal planar graph will be triangular.(b) If a connected, maximal planar graph has n vertices, how many regions andedges does it have?
3. Travel Nicole wants to tour Asia. She will start and end her journey in Tokyo and visit HongKong, Bangkok, Seoul, and Beijing. The airfares available to her betweencities are given in the table. Draw a weighted graph that represents the travel costs between cities and use thealgorithm to find a low-cost route. Highlight/color the edges to show the circuit.
A chicken farmer wishes to provide electric power to each chicken house on his farm by installing buried electrical power lines. The graph below illustrates the locations of the houses and the distances between them in feet. Use Kruskal's algorithm to determine how the farmer should dig channels in order to minimize the amount of digging. Also determine the minimum total length of channels that must be dug.

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