Graphs

1
Graphs Trees

• Introductory Discrete Mathematics (CS/MAT165)

2
Graphs

• A graph consists of two finite sets
• V(G), a set vertices
• E(G), a set of edges, where each edge is
  represented by an unordered pair of vertices

3
Try this!
v1
v1
v1
v1

• Determine the vertex and edge sets for this graph

4
Dirceted Graphs

• A directed graph consists of two finite sets
• V(G), a set vertices
• D(G), a set of edges, where each edge is
  represented by an ordered pair of vertices

5
Try this!
v1
v1
v1
v1

• Determine the vertex and edge sets for this graph

6
Graphs

• Simple graph
• No loops or parallel edges
• Complete graph
• One edge for each pair of vertices

7
Problems

• PP. 662-663, Nos. 3, 5, 15, 19, 26

8
The Bridges of Könisberg

• The city of Königsberg, Prussia (now Kaliningrad,
  Russia) is set on the Pregel River, and included
  two large islands which were connected to each
  other and the mainland by seven bridges
• Is it possible to walk with a route that crosses
  each bridge exactly once?