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.
Chapter2: Parallel Lines
Section2.5: Convex Polygons
Problem 41E
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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?

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