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Draw an undirected graph that has exactly 11 edges and at least 5 vertices, in which two of the vertices have degree exactly 4, three of the vertices have degree exactly 3, and all other vertices have degree at most 2. Use as few vertices as possible and prove that you cannot use fewer vertices.

Draw an undirected graph that has exactly 11 edges and at least 5 vertices, in which two of the vertices have degree exactly 4, three of the vertices have degree exactly 3, and all other vertices have degree at most 2. Use as few vertices as possible and prove that you cannot use fewer vertices.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Draw an undirected graph that has exactly 11 edges and at least 5 vertices, in which two of the vertices have degree exactly 4, three of the vertices have degree exactly 3, and all other vertices have degree at most 2. Use as few vertices as possible and prove that you cannot use fewer vertices.
Transcribed Image Text:Draw an undirected graph that has exactly 11 edges and at least 5 vertices, in which two of the vertices have degree exactly 4, three of the vertices have degree exactly 3, and all other vertices have degree at most 2. Use as few vertices as possible and prove that you cannot use fewer vertices.
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