Represent the following map with a graph. VA KY TN NC OA. Owv O B. KY VA KY VA TN NC TN NC
Represent the following map with a graph. VA KY TN NC OA. Owv O B. KY VA KY VA TN NC TN NC
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:Title: Graph Representation of a Map
Description: The image illustrates a map with five regions: KY (Kentucky), WV (West Virginia), VA (Virginia), TN (Tennessee), and NC (North Carolina). The task is to represent this map using a graph.
Image Details:
1. **Map Representation**:
- The map shows the five regions.
- The borders between these regions are clearly marked.
2. **Graph Options**:
**Option A**:
- This graph uses nodes labeled KY, WV, VA, TN, and NC.
- Connections reflect the shared borders between regions:
- KY is connected to WV and TN.
- WV is connected to VA.
- VA is connected to NC.
- NC is connected to TN.
**Option B**:
- This graph also uses nodes labeled KY, WV, VA, TN, and NC.
- Connections are as follows:
- KY is connected to WV, VA, and TN.
- WV is connected to VA and TN.
- VA is connected to NC.
- NC is connected to TN.
Expert Solution
Step 1
Given:
States: WV, VA, NC, TN, KY
consider them as vertices,
and border between them represents the edges.
Step 2
Explanation:
Since there are 5 vertices
and according to the map there are 7 edges ( borders).
Since one state is connected with other state with border,
1] Consider WV connected with VA and KY . (with borders in common)
2] VA connected with KY and NC
3] NC connected with VA and TN
4] TN connected with VA and KY
5] KY connected with VA and WV
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