Defined basic graph theory terms such as graph, vertices, edges, order, size, degree of vertices, complete graph and equivalent graph. Defined and discussed Euler’s path and Euler’s circuit. Defined and discussed weighted graph

1. THE MATHEMATICS
OF THE GRAPH
Group 5

2. LEARNING OUTCOME
• Defined basic graph theory terms such as graph, vertices, edges, order, size,
degree of vertices, complete graph and equivalent graph.
• Defined and discussed Euler’s path and Euler’s circuit.
• Defined and discussed weighted graph

3. Introduction
Graphs are very important in our lives. It is used to represent and solve
problems in our real life situation such as places connected to roads, or road
maps, bridges, relationship of people, electrical networks, football teams, links of
websites, flow of computations, data organization and many more.

4. Key concept
• Graph is a set of finite set of points called vertices and line segments or
curves called edges that connect vertices.
• Euler Path is a path that passes through every edge exactly once.
• Euler Circuit is a circuit that passes every edge exactly once.
• Weighted Graph is a graph in which it is associated with the value, called a
weight. The average of an edge can represent also the cost or distance, the
amount effort needed to travel from one place to another.

5. The graph is made up of vertices (nodes) that are connected
by the edges (lines).
Examples:
Graph
Legend
Edge or line
Vertices (nodes)

6. Examples of graph
1. Null or Disconnected Graph. The graph below is a null or disconnected graph since it has four
vertices but no edges. The degree of each vertex is 0.
2. Graph with loop. The loop connects vertex to itself. The degree of a loop is 2
3. Graph with multiple edges

7. Basic types of graph