Mathematics · Graph Theory
Suppose G is a graph with n vertices such that every vertex has degree 5. What is the minimum number of edges in terms of n, and what is the smallest number of vertices n for which G could possibly be a planar graph?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Number of edges e = 2n5; Smallest n = 10
- 2Number of edges e = 2n; Smallest n = 12
- 3Number of edges e = 5n; Smallest n = 6
- 4Number of edges e = 5n2; Planar graph is impossible for any 5-regular graph.✓
Correct answer
Number of edges e = 5n2; Planar graph is impossible for any 5-regular graph.
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