Question 4 (20 points): You are given n cities that are connected by a network of k highways. A highway is defined to be a road between two cities that does not go through any intermediate cities. Two cities can have at most one highway directly connecting them (therefore, the highway network is not a multigraph) Show that if k > 1/2(n - 1)(n - 2), then one can always travel between any two cities through connecting highways.
Added by Henry K.
Close
Step 1
This will require (n-1) highways. ** Show more…
Show all steps
Your feedback will help us improve your experience
Arjun Khokher and 98 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Assuming that the amount of traffic flowing into a junction must equal the amount of traffic flowing out of the junction, write a system of linear equations that describes the flow of traffic for the following diagram. You only need to set up the equations, not solve them.
Amanda C.
Prove that a connected graph of order $n \geq 2$ has at least two vertices that are not articulation vertices. (Hint: Take the two end vertices of a longest path.)
Nick J.
Show that a simple graph $G$ with $n$ vertices is connected if it has more than $(n-1)(n-2) / 2$ edges.
Graphs
Connectivity
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD