Introduction to Graph Theory
Explore fundamental concepts in graph theory including vertices, edges, degrees, and types of graphs with this grade 9 math worksheet.
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Introduction to Graph Theory
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Read each question carefully and answer to the best of your ability. Show all your work where applicable.
1. In graph theory, a graph is composed of a set of (also called nodes) and a set of that connect pairs of these elements.
2. The of a vertex is the number of edges incident to it.
3. A graph where all edges are undirected is called an graph.
Consider the following graph:
4. List all the vertices in the graph.
5. List all the edges in the graph.
6. Determine the degree of each vertex.
7. Which of the following best describes a simple graph?
A graph with multiple edges between the same pair of vertices.
A graph with no loops and no multiple edges between any two vertices.
A graph where edges have a direction.
A graph where vertices are connected in a cyclic manner.
8. What is the maximum number of edges in a simple graph with 4 vertices?
3
4
6
12
9. A directed graph (digraph) has edges with a specific direction.
True
False
10. A complete graph is a simple graph in which every pair of distinct vertices is connected by a unique edge.
True
False
11. Draw a simple graph with 5 vertices and 6 edges. Label your vertices and edges clearly.