There is a funny thing that occurs in mathematics where eigenvalues of various adjacency matrices of graphs capture information about the graph. Trivially, they give the number of vertices and edges of a graph. Less trivially, eigenvalues give bounds on the chromatic number, coclique number and other graph invariants. It is conjectured by Haemers that the eigenvalues of a graph almost always determines the isomorphism class.
This semester (Spring 2013), I am organising a learning seminar on the algebraic graph theory of J.J. Seidel. We will cover topics including two-graphs, strongly regular graphs and matrices relating to combinatorial properties of graphs. No prior background in algebraic graph theory will be assumed; during the course of the seminar, we will present a basic introduction to spectral graph theory. It will be a 2-hour per week seminar.
The seminar will follow the book Geometry and Combinatorics: Selected Works of J.J. Seidel, edited by D.G. Corneil and R. Mathon. We will present a paper each week.
Below is the schedule of talks. All talks are at 12:30 pm to 2:30 pm unless specified.
|Date||Title of Paper||Speaker|
|January 25, 2013||A Survey of Two Graphs, J.J. Seidel, 1976||Krystal Guo|
|February 1, 2013||Equiangular Lines, P.W.H. Lemmens and J.J. Seidel, 1971||Matt DeVos|
|February 8, 2013||Quadratic Forms Over GF(2), P.J. Cameron and J.J. Seidel, 1972||Krystal Guo|
|February 15, 2013||The Regular Two-Graph on 276 Vertices, J.M. Goethals and J.J. Seidel, 1974||Tony Huynh|
|February 22, 2013||Bounds for Systems of Lines, and Jacobi Polynomials, P. Delsarte, P.J. Cameron and J.J. Seidel, 1976||Karen Yeats|
|March 1, 2013||Line Graphs, Root Systems, and Elliptic Geometry, P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, 1976||Avi Kulkarni|
|March 8, 2013||Strongly Regular Graphs with (-1,1,0) Adjacency Matrix Having Eigenvalue 3, Seidel, 1968.||Krystal Guo|
|March 15, 2013||Strongly Regular Graphs Having Strongly Regular Subconsituents, P.J. Cameron, J.M. Goethals, and J.J. Seidel, 1977.||Krystal Guo|
|March 22, 2013||Equi-isoclinic subspaces of Euclidean spaces, P.W.H. Lemmens and J.J. Seidel, 1973.||Krystal Guo|
|March 29, 2013||Easter Weekend (no seminar)|
|April 5, 2013||Spherical Codes and Designs, P. Delsarte, J.M. Goethals and J.J. Seidel, 1977.||Matt DeVos|
|April 12, 2013||Part 2 of previous week||Matt DeVos|
|April 19, 2013||The Krein Condition, Spherical Designs, Norton Algebras and Permutation Groups, P. Delsarte, J.M. Goethals and J.J. Seidel, 1978.||Krystal Guo|