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4. This problem is about graphs. In each of the following cases, either draw a graph with the stated property, or prove that no such graph exists. (For the purpose of this problem, a “graph" must have no loops or multiple edges.) (a) A graph on 12 vertices in which every vertex has degree 4. (b) A graph on 45 vertices in which 22 vertices have degree 8 and 23 vertices have degree 7. (c) A graph on 10 vertices in which every vertex has degree 3 and the shortest cycle subgraph has length 5. (d) A graph on 13 vertices in which every vertex has degree at least 7 and there are no cycle subgraphs of length 3.

4. This problem is about graphs. In each of the following cases, either draw a graph with the stated property, or prove that no such graph exists. (For the purpose of this problem, a “graph" must have no loops or multiple edges.) (a) A graph on 12 vertices in which every vertex has degree 4. (b) A graph on 45 vertices in which 22 vertices have degree 8 and 23 vertices have degree 7. (c) A graph on 10 vertices in which every vertex has degree 3 and the shortest cycle subgraph has length 5. (d) A graph on 13 vertices in which every vertex has degree at least 7 and there are no cycle subgraphs of length 3.

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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4. This problem is about graphs. In each of the following cases, either draw a graph with the stated property, or prove that no such graph exists. (For the purpose of this problem, a “graph" must have no loops or multiple edges.) (a) A graph on 12 vertices in which every vertex has degree 4. (b) A graph on 45 vertices in which 22 vertices have degree 8 and 23 vertices have degree 7. (c) A graph on 10 vertices in which every vertex has degree 3 and the shortest cycle subgraph has length 5. (d) A graph on 13 vertices in which every vertex has degree at least 7 and there are no cycle subgraphs of length 3.
Transcribed Image Text:4. This problem is about graphs. In each of the following cases, either draw a graph with the stated property, or prove that no such graph exists. (For the purpose of this problem, a “graph" must have no loops or multiple edges.) (a) A graph on 12 vertices in which every vertex has degree 4. (b) A graph on 45 vertices in which 22 vertices have degree 8 and 23 vertices have degree 7. (c) A graph on 10 vertices in which every vertex has degree 3 and the shortest cycle subgraph has length 5. (d) A graph on 13 vertices in which every vertex has degree at least 7 and there are no cycle subgraphs of length 3.
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