Graph Theory Fundamentals
Explore the basic concepts of graph theory, including vertices, edges, paths, and cycles, with this Grade 10 math worksheet.
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Graph Theory Fundamentals
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Read each question carefully and answer to the best of your ability. Show all your work where applicable.
1. Which of the following best describes a 'vertex' in graph theory?
A line connecting two points
A point where lines meet
A closed loop in a graph
A numerical value assigned to a graph
2. What is the maximum number of edges in a simple graph with 4 vertices?
3
4
6
8
3. A graph that has no loops and no multiple edges between the same pair of vertices is called a graph.
4. The of a vertex is the number of edges incident to it.
5. Consider the following graph:
List all the vertices and edges in the graph above. (Use standard notation, e.g., (A,B) for an edge)
6. A path in a graph can visit the same vertex more than once.
True
False
7. A cycle in a graph must start and end at the same vertex.
True
False
8. Draw a simple graph with 5 vertices and 6 edges. Ensure the graph contains at least one cycle and one isolated vertex. Label your vertices.