Discrete Mathematics Project

Graph Theory Activity


Bus Route (Ed Snyder)


(1) Students will begin to explore the concept of route design and finding the shortest route as it pertains to graph theory.

(2) Students will work in small groups for the purpose of finding the shortest bus route, then graphing the shortest route.


This activity is designed for students to design a new bus route in their neighborhood. It is important to link the concept of route planning to graph theory as it relates to discrete mathematics.

Problem Statement

Suggest to students that designing routes is a challenge for many different industries. Ask students to brainstorm on how many different industries use routes as a necessity of their business. Also discuss how important it is to utilize the shortest route possible and what kind of economical impacts it would have on that industry.

Instructor Suggestions

(1) Begin by discussing the problem statement.

(2) Have students form small groups.

(3) Distribute the Bus Route activity sheet and have students work on the problem.

(4) Have each group select a spokesperson to report their findings to the class.

(5) Discuss students results as it relates to graph theory.


"Bus Route" activity sheet, chalkboard, or overhead projector and transparencies.


Introduction (5 min.), group work( 25 min.), presentation of group work and class discussion (20 min.)

Mathematics Concepts

Discrete Mathematics Concepts

Graph theory including, critical paths, Euler Circuits/ Paths, Hamiltonian Circuits/ Paths,

Related Mathematics Concepts

Geometrical concepts including vertices , edges, Sequences, Series.

NCTM Standards Addressed

Problem solving, Communications, Reasoning, Discrete Mathematics.

Colorado Model Content Standards Addressed

Data Collection and Analysis (3), Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This particular activity could be integrated into a Integrated (1) Mathematics course during a graphing or geometry unit.

Further Investigation

The assignment can be extended by having students design their own route for one of the other industries discussed in the problem statement.



Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W. H. Freeman and Company.

Kenney, M.J., & Hirsch, C. R. (Eds.). (1991). Discrete mathematics across the curriculum, K-12. Reston. VA; National Council of Teachers of Mathematics.

Last updated January 16, 1997