Euler Circuit

Euler's Theorem

a graph has an Euler Circuit if: 1) the graph is connected AND 2) all vertices have a valence number that is even

connected

a graph in one piece OR when you can travel from one vertex to all other vertices using a path

edge

a link that connects two different vertices

Edge-Walker Technique

a method to find an efficient Eulerization to a rectangular network by traveling the perimeter of the graph

circuit

a path that starts and stops at the same vertex

Euler Circuit

a path that starts and stops at the same vertex, but touches each edge only once

vertex

a dot that represents a location, intersection, city, etc...

graph

a finite set of vertices and connecting edges

path

a connecting sequence of edges that starts at one vertex and ends at a different vertex

valence

the number of edges that meet at a vertex

Eulerizing

to 'add' edges to a graph that does not contain an Euler Circuit

Chinese Postman Problem

trying to find the minimum number of edges needed to retrace in order to find an Euler Circuit on a graph that does not have one originally

digraph

when edges have arrows indicating how you can travel around the graph

Euler Path

when you travel each edge only once, but start and stop at different vertices