Topic: Introduction to Graph Theory.
Objectives: Students will be able
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a) to define a graph, and a null graph.
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b) to differentiate between graphs, null graphs and drawings that not graphs.
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c) to identify the parts of a graph.
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d) to identify a digraph.
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e) to use a graph to represent a problem.
Prerequisites:
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a) Plot points
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b) Draw straight lines.
Skills and concepts presented:
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a) Plotting and joining points
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b) organizing information.
Developments:
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1. Develop a dialogue that would show the students the importance that drawing a diagram (in this case graphs) in solving problems.
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2. Point out that graphs are considered as models and therefore can be used to represent a situation.
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3. Introduce the airline problem from the content.
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4. Introduce and explain each step:
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i) how to organize the information in a table.
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ii) introduce vertex or nodes and edges.
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iii) give examples of null graphs, graphs, and drawings that are not graphs
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5. Formally define graphs and digraphs.
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6. Present drill and practice for students to use the information discussed.
Possible Problems for discussion:
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1. In the following sketches identify the vertices and the edges.
(figure available in print form)
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2. Identify each of the following as graphs or not a graph.
(figure available in print form)
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3. a) Draw a complete graph with six vertices.
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b) How many edges are there?
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4. Draw a null graph with eight vertices.
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5. Draw a graph to show the friendship relation among four individuals.
Extension Activities:
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1. Have students suggest possible problems from which they can produce a graph.
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2. Have students draw a digraph of friendship relation in the classroom.
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3. The following are dependent statements (implications exist between them):
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a) The Wright brothers first flight.
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b) Better aircrafts invented.
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c) More jobs provided.
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d) Standard of living improved.
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e) More people take trips on airplanes.
Draw a digraph to show the relationship between the statements.
