1. Module 5 – Networks and Decision Mathematics Chapter 23 – Undirected Graphs

2. 23.2 Planar Graphs and Euler’s Formula A graph that can be drawn in such a way that no two edges meet or cross (or have common points) except the vertices where they join, is called a planar graph. Not all graphs are planar however some can be redrawn so that no two edges cross each other. Insert graphs Note: the vertices do not change location. Edges are adjusted only.

3. Eulers’ formula (pronounced Oiler), states that for any connected planar graph, v – e + f = 2 Where: v = number of vertices e = number of edges f = number of faces (regions)

4. When calculating the number of faces/regions for any network, the outer region is also included Insert graphs The outer face denotes an infinite face or region Example: Given the graph below, verify that it is planar using Euler’s Rule. Insert example graph and steps