Math Problem Statement
Solution
The image contains a mathematical problem with a directed and weighted graph in minutes, as well as questions regarding the graph.
Here are the details from the image:
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Graph Description:
The diagram represents a graph with four transit stations: , , , and . Edges between these stations are labeled with weights, which denote the time in minutes for transit. There is also a fixed transit stop time of 5 minutes at each station. -
Questions:
- (a) Draw a spanning tree based on the graph.
- (b) Emelda takes the commuter train from to . Calculate the shortest time route.
To Solve:
(a) Draw a Spanning Tree:
A spanning tree is a subgraph that connects all the vertices together without any cycles and with the minimum number of edges.
(b) Shortest Route Calculation:
Use the shortest path algorithm (e.g., Dijkstra's Algorithm) to calculate the route from to considering the weights of the edges.
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Math Problem Analysis
Mathematical Concepts
Graph Theory
Weighted Graphs
Spanning Tree
Shortest Path
Formulas
Dijkstra's Algorithm for shortest path
Theorems
Graph connectivity theorem
Suitable Grade Level
Grades 9-12
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