Standard 2 : Graph Theory (Archived)



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Understand how graphs of vertices joined by edges can model relationships and can be used to solve various problems with relation to directed graphs, weighted graphs, networks, tournaments, transportation flows, matching, and coverage.

General Information

Number: MA.912.D.2
Title: Graph Theory
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Discrete Mathematics

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.D.2.1: Use Euler and Hamilton cycles and paths in graphs to solve routing problems.
MA.912.D.2.2: Use critical path analysis to solve scheduling problems.
MA.912.D.2.3: Use graph coloring techniques to solve problems.
MA.912.D.2.4: Use spanning trees, rooted trees, binary trees, and decision trees to solve problems.
MA.912.D.2.5: Use bin-packing techniques to solve problems concerning optimizing resource usage.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plans

Name Description
Who Do You Know? The Theory Behind Social Networking:

This video lesson will introduce students to algorithmic thinking through the use of a popular field in graph theory—social networking. Specifically, by acting as nodes in a graph (i.e. people in a social network), the students will experientially gain an understanding of graph theory terminology and distance in a graph (i.e. number of introductions required to meet a target person). Once the idea of distance in a graph has been built, the students will discover Dijkstra's Algorithm. The lesson should take approximately 90 minutes and can be comfortably partitioned across two class sessions if necessary (see the note in the accompanying Teacher Guide). There are no special supplies needed for this class and all necessary hand-outs can be downloaded from this website.

Visualization of Social Networks with Node Graphs:

This lesson introduces the concept of node graphs for the purpose of visualizing social networks.

The lesson is presented with an introductory physical activity where students create a living graph. Students, building on their existing knowledge regarding common graph types, learn how node graphs can be used to visualize data from social networks.

Students will then participate in a simulated contagious infection event and will accurately record data about the transmission of the disease. These data will be used to construct a single computer file to be used to create a single node graph for describing the network. Students will then be responsible for understanding how to interpret the resulting network graph in the context of the activity.