Section 1: The language of graphs Key point 1.1 A graph is a set of vertices connected by edges. A vertex is shown as a point on a graph. Vertices are sometimes labelled, and sometimes not. An edge is a line or curve with a vertex at each end.
PL E
WORKED EXAMPLE 1.1
a List the vertices in this graph. b List the edges in the graph. a The vertices are A, , C , D and E.
AB, AC , AD, BC
and BE.
You can identify an edge by the vertices at its ends. Edge BA is the same as edge AB, for example.
Key point 1.2
SA
b
Not all graphs will have labelled vertices.
M
B
A walk is a set of edges joined end to end, so the end vertex of one edge is the start vertex of the next. A trail is a walk in which no edges are repeated. Vertices can be repeated in a trail, although often they are not. A cycle is a trail that starts and finishes at the same vertex. Other than the start being the same as the finish, vertices are not repeated in a cycle.
Fast forward The terms trail and cycle will be used in route inspection problems and the travelling salesperson problem in Chapter 2.
Original material Š Cambridge University Press 2018