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b) An undirected graph is n-regular if all vertices have degree n. For example, the graphs below are both 3-regular because each vertex is attached to three edges. FIGURE 1. Two 3-regular graphs. Draw a few of these. For example, can you find a 2-regular graph with 4 vertices? A 3-regular one? A 4-regular one? What about a 3-regular graph with 5 vertices? Is there a 2-regular graph with 5 vertices? Use induction to show that for every n 2 1 there exists an n-regular graph.

b) An undirected graph is n-regular if all vertices have degree n. For example, the graphs below are both 3-regular because each vertex is attached to three edges. FIGURE 1. Two 3-regular graphs. Draw a few of these. For example, can you find a 2-regular graph with 4 vertices? A 3-regular one? A 4-regular one? What about a 3-regular graph with 5 vertices? Is there a 2-regular graph with 5 vertices? Use induction to show that for every n 2 1 there exists an n-regular graph.

Advanced Engineering Mathematics
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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b) An undirected graph is n-regular if all vertices have degree n. For example, the graphs below are both 3-regular because each vertex is attached to three edges. FIGURE 1. Two 3-regular graphs. Draw a few of these. For example, can you find a 2-regular graph with 4 vertices? A 3-regular one? A 4-regular one? What about a 3-regular graph with 5 vertices? Is there a 2-regular graph with 5 vertices? Use induction to show that for every n 2 1 there exists an n-regular graph.
Transcribed Image Text:b) An undirected graph is n-regular if all vertices have degree n. For example, the graphs below are both 3-regular because each vertex is attached to three edges. FIGURE 1. Two 3-regular graphs. Draw a few of these. For example, can you find a 2-regular graph with 4 vertices? A 3-regular one? A 4-regular one? What about a 3-regular graph with 5 vertices? Is there a 2-regular graph with 5 vertices? Use induction to show that for every n 2 1 there exists an n-regular graph.
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