Discovering Graph Theory Relationships Using a Graph Database Jason - - PowerPoint PPT Presentation

Discovering Graph Theory Relationships Using a Graph Database

Jason Grout

Department of Mathematics Brigham Young University

Mathfest 2005

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 1 / 8

Outline

1

Graph Database

2

The Vision

3

Potential Problems

4

Summary

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 2 / 8

Graph Database http://math.byu.edu/~grout/graphs

All (13,598) graphs up through 8 vertices. Includes data on most major graph invariants. Includes pictures of graphs. Easily searchable. I can email you several pages of exercises to use with the database.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 3 / 8

Graph Database http://math.byu.edu/~grout/graphs

All (13,598) graphs up through 8 vertices. Includes data on most major graph invariants. Includes pictures of graphs. Easily searchable. I can email you several pages of exercises to use with the database.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 3 / 8

Graph Database http://math.byu.edu/~grout/graphs

All (13,598) graphs up through 8 vertices. Includes data on most major graph invariants. Includes pictures of graphs. Easily searchable. I can email you several pages of exercises to use with the database.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 3 / 8

Graph Database http://math.byu.edu/~grout/graphs

All (13,598) graphs up through 8 vertices. Includes data on most major graph invariants. Includes pictures of graphs. Easily searchable. I can email you several pages of exercises to use with the database.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 3 / 8

Graph Database http://math.byu.edu/~grout/graphs

All (13,598) graphs up through 8 vertices. Includes data on most major graph invariants. Includes pictures of graphs. Easily searchable. I can email you several pages of exercises to use with the database.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 3 / 8

Graph Database http://math.byu.edu/~grout/graphs

All (13,598) graphs up through 8 vertices. Includes data on most major graph invariants. Includes pictures of graphs. Easily searchable. I can email you several pages of exercises to use with the database.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 3 / 8

The Vision

Students are Motivated and exploring examples; Conjecturing relationships; Proving or disproving conjectures; Checking their work.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 4 / 8

The Vision

Students are Motivated and exploring examples; Conjecturing relationships; Proving or disproving conjectures; Checking their work.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 4 / 8

The Vision

Students are Motivated and exploring examples; Conjecturing relationships; Proving or disproving conjectures; Checking their work.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 4 / 8

The Vision

Students are Motivated and exploring examples; Conjecturing relationships; Proving or disproving conjectures; Checking their work.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 4 / 8

Potential Problem: Arbitrary Relationships

Relationships can seem arbitrary and unmotivated.

Example

The sum of the degrees of the vertices is twice the number of edges.

Example

If G is connected and planar with v ≥ 3 vertices and e edges, and G has no induced triangles, then e ≤ 2v − 4.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 5 / 8

Potential Problem: Arbitrary Relationships

Relationships can seem arbitrary and unmotivated.

Example

The sum of the degrees of the vertices is twice the number of edges.

Example

If G is connected and planar with v ≥ 3 vertices and e edges, and G has no induced triangles, then e ≤ 2v − 4.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 5 / 8

Potential Problem: Large Data Sets

Large data sets make conjecturing difficult.

Example

Conjecture and prove a relationship between the degrees of a graph and whether the graph is Eulerian or not. (Only 15 out of the 143 connected graphs on 6 or less vertices are Eulerian).

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 6 / 8

Potential Problem: Large Data Sets

Large data sets make conjecturing difficult.

Example

Conjecture and prove a relationship between the degrees of a graph and whether the graph is Eulerian or not. (Only 15 out of the 143 connected graphs on 6 or less vertices are Eulerian).

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 6 / 8

Potential Problem: Checking Work

There is no outside source to check work.

Example

Determine whether a given 8 vertex graph is planar.

Example

Find all the Hamiltonian cycles in a given graph.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 7 / 8

Potential Problem: Checking Work

There is no outside source to check work.

Example

Determine whether a given 8 vertex graph is planar.

Example

Find all the Hamiltonian cycles in a given graph.

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 7 / 8

Summary

The graph database can help with the problems of: Motivating students to conjecture relationships; Exploring large numbers of examples easily; Checking work.

http://math.byu.edu/~grout/graphs

Jason Grout (grout@math.byu.edu) http://math.byu.edu/~grout/graphs Mathfest 2005 8 / 8