Triangle graph

The Goldner – Harary graph is maximally planar. Each area is surrounded by three edges.

A triangulation is in Graph theory , a planar graph , in which each of its regions by a circle of length is boxed. A triangle graph therefore has at least three nodes. ${\displaystyle 3}$

A maximally planar graph (or maximally planar graph ) is a planar graph to which no edge can be added without losing its planarity. Every graph with at least three nodes is maximally planar if and only if it is a triangle graph.

A triangle graph with nodes has exactly edges and regions. The smallest triangle graph is the circle graph consisting of exactly three nodes. ${\displaystyle n}$ ${\displaystyle 3n-6}$ ${\displaystyle 2n-4}$ ${\displaystyle C_{3}}$

literature

• Reinhard Diestel: graph theory . Springer, 2006, ISBN 3-540-21391-0 ( limited preview in Google book search).