Summary: Graph Theory Worksheet Math 105, Fall 2010 Page 1
Paths and Circuits
Path: a sequence of adjacent edges, where the edges used are used only once.
Length: the number of edges in the path.
Connected: a graph in which a path exists between any two vertices.
Disconnected: not connected!
Components: connected parts of the graph.
Circuit: a path that starts and ends at the same vertex.
Euler Path: a path in a connected graph that passes through every edge of the graph once
and only once.
Euler Circuit: a path in a connected graph that starts and ends at the same vertex, and
passes through every edge of the graph once and only once.