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Graph Theory Fundamentals

Explore the basic concepts of graph theory, including vertices, edges, paths, and cycles, with this Grade 10 math worksheet.

Grade 10 Math Data and GraphingGraph Theory
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Includes

Multiple ChoiceFill in the BlanksShort AnswerTrue / FalseLong Answer

Standards

CCSS.MATH.CONTENT.HSG.CO.D.12

Topics

Graph TheoryMathematicsGrade 10GraphsVerticesEdges
7 sections · Free to use · Printable
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Graph Theory Fundamentals

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Date:

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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

A line connecting two points

b

A point where lines meet

c

A closed loop in a graph

d

A numerical value assigned to a graph

2. What is the maximum number of edges in a simple graph with 4 vertices?

a

3

b

4

c

6

d

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:

A B C D

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.

T

True

F

False

7. A cycle in a graph must start and end at the same vertex.

T

True

F

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.