14) A graph G is called maximal planar if G is planar but the addition of another edge between two nonadjacent vertices will make the graph nonplanar. (a) Show that every region of a connected, maximal planar graph will be triangular. (b) If a connected, maximal planar graph has n vertices, how many regions and edges does it have?

14) A graph G is called maximal planar if G is planar but the addition of another edge between two nonadjacent vertices will make the graph nonplanar. (a) Show that every region of a connected, maximal planar graph will be triangular. (b) If a connected, maximal planar graph has n vertices, how many regions and edges does it have?

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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