9. A planar graph has faces (including the external face) composed of eight 3-cycles and eighteen 4- cycles. The graph is regular, that is the degree of all vertices are the same, and the same number of 4-cycles and 3-cycles meet at each vertex. (a) How many vertices and how many edges does it have? Explain. (b) How many 4-cycles and how many 3-cycles meet at each vertex? Explain. (Hint: it might help to think of 3-cycles as triangles and 4-cycles as squares.)
9. A planar graph has faces (including the external face) composed of eight 3-cycles and eighteen 4- cycles. The graph is regular, that is the degree of all vertices are the same, and the same number of 4-cycles and 3-cycles meet at each vertex. (a) How many vertices and how many edges does it have? Explain. (b) How many 4-cycles and how many 3-cycles meet at each vertex? Explain. (Hint: it might help to think of 3-cycles as triangles and 4-cycles as squares.)
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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