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If we were to add edges (L, I), (I, G), (G,E), (E, C), (C, L) then would this graph have an Euler path? If it does, draw arrows indicating the path. If it does not, explain why not.

If we were to add edges (L, I), (I, G), (G,E), (E, C), (C, L) then would this graph have an Euler path? If it does, draw arrows indicating the path. If it does not, explain why not.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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The class I'm taking is computer science discrete structures. 

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**Graph Explanation and Problem Solution** The given image shows a graph with 12 vertices labeled from A to L, interconnected by edges. Here are the vertices and their connections: - Vertex A is connected to B, D, F, and J. - Vertex B is connected to A and C. - Vertex C is connected to B. - Vertex D is connected to A and E. - Vertex E is connected to D. - Vertex F is connected to A and G. - Vertex G is connected to F. - Vertex H is connected to A and I. - Vertex I is connected to H. - Vertex J is connected to A, K, and L. - Vertex K is connected to J. - Vertex L is connected to J. **Problem Statement:** The task is to determine if adding the following edges: (L, I), (I, G), (G, E), (E, C), (C, L), would result in a graph that has an Euler path. An Euler path is a trail in a graph that visits every edge exactly once. **Solution:** To have an Euler path, a graph can have at most two vertices with an odd degree. By adding the new edges, consider: - **Degree Changes:** - L connects to I and C: L’s degree initially 1, becomes 3 (odd). - I connects to L and G: I’s degree initially 1, becomes 3 (odd). - G connects to I and E: G’s degree initially 1, becomes 3 (odd). - E connects to G and C: E’s degree initially 1, becomes 3 (odd). - C connects to E and L: C’s degree initially 1, becomes 3 (odd). All vertices with edges have odd degrees. Adding these edges results in a graph where more than two vertices have an odd degree, meaning the graph does not have an Euler path. **Conclusion:** Adding the specified edges results in a graph with more than two vertices of odd degree, making an Euler path impossible.
Transcribed Image Text:**Graph Explanation and Problem Solution** The given image shows a graph with 12 vertices labeled from A to L, interconnected by edges. Here are the vertices and their connections: - Vertex A is connected to B, D, F, and J. - Vertex B is connected to A and C. - Vertex C is connected to B. - Vertex D is connected to A and E. - Vertex E is connected to D. - Vertex F is connected to A and G. - Vertex G is connected to F. - Vertex H is connected to A and I. - Vertex I is connected to H. - Vertex J is connected to A, K, and L. - Vertex K is connected to J. - Vertex L is connected to J. **Problem Statement:** The task is to determine if adding the following edges: (L, I), (I, G), (G, E), (E, C), (C, L), would result in a graph that has an Euler path. An Euler path is a trail in a graph that visits every edge exactly once. **Solution:** To have an Euler path, a graph can have at most two vertices with an odd degree. By adding the new edges, consider: - **Degree Changes:** - L connects to I and C: L’s degree initially 1, becomes 3 (odd). - I connects to L and G: I’s degree initially 1, becomes 3 (odd). - G connects to I and E: G’s degree initially 1, becomes 3 (odd). - E connects to G and C: E’s degree initially 1, becomes 3 (odd). - C connects to E and L: C’s degree initially 1, becomes 3 (odd). All vertices with edges have odd degrees. Adding these edges results in a graph where more than two vertices have an odd degree, meaning the graph does not have an Euler path. **Conclusion:** Adding the specified edges results in a graph with more than two vertices of odd degree, making an Euler path impossible.
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