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Discovering Graph Theory Relationships Using a Graph Database Jason Grout Department of Mathematics Brigham Young University Mathfest 2005 Jason Grout (grout@math.byu.edu) Mathfest 2005 1 / 8 http://math.byu.edu/~grout/graphs Outline

Discovering Graph Theory Relationships Using a Graph Database Jason Grout Department of Mathematics Brigham Young University Mathfest 2005 Jason Grout (grout@math.byu.edu) Mathfest 2005 1 / 8 http://math.byu.edu/~grout/graphs
Outline Graph Database 1 The Vision 2 Potential Problems 3 Summary 4 Jason Grout (grout@math.byu.edu) Mathfest 2005 2 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 3 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 3 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 3 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 3 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 3 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 3 / 8 http://math.byu.edu/~grout/graphs
The Vision Students are Motivated and exploring examples; Conjecturing relationships; Proving or disproving conjectures; Checking their work. Jason Grout (grout@math.byu.edu) Mathfest 2005 4 / 8 http://math.byu.edu/~grout/graphs
The Vision Students are Motivated and exploring examples; Conjecturing relationships; Proving or disproving conjectures; Checking their work. Jason Grout (grout@math.byu.edu) Mathfest 2005 4 / 8 http://math.byu.edu/~grout/graphs
The Vision Students are Motivated and exploring examples; Conjecturing relationships; Proving or disproving conjectures; Checking their work. Jason Grout (grout@math.byu.edu) Mathfest 2005 4 / 8 http://math.byu.edu/~grout/graphs
The Vision Students are Motivated and exploring examples; Conjecturing relationships; Proving or disproving conjectures; Checking their work. Jason Grout (grout@math.byu.edu) Mathfest 2005 4 / 8 http://math.byu.edu/~grout/graphs
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 ≤ 2 v − 4. Jason Grout (grout@math.byu.edu) Mathfest 2005 5 / 8 http://math.byu.edu/~grout/graphs
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 ≤ 2 v − 4. Jason Grout (grout@math.byu.edu) Mathfest 2005 5 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 6 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 6 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 7 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 7 / 8 http://math.byu.edu/~grout/graphs
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) Mathfest 2005 8 / 8 http://math.byu.edu/~grout/graphs

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