On Classifying Finite Edge Colored Graphs with Doubly Transitive Automorphism Groups
Thomas Q. Sibley
St. John's University
Febrary 24,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

We can represent metrical, linear and other geometrical
structure on a set by coloring the edges of the complete graph
whose vertices are the elements of the set. For a metric
space (X,d), we can color edges st and uv the same iff
d(s,t) = d(u,v). If every two vertices determine a unique
line, we can alternatively color edges st and uv the same iff
s and t determine the same line as u and v. An automorphism
permutes the vertices and the colors. Thus, for example, the
similarities are the automorphisms for R^n with the Euclidean
metric coloring and the affine transformations are the
automorphisms for R^n with the linear coloring. Both of these
groups of automorphisms are doubly transitive on the vertices.
The classification of finite doubly transitive edge colored
graphs is complete when the group of automorphisms contains a
doubly transitive simple group. We will present the known
results, partial results and conjectures with regard to this
classification and consider its connections with other work.

Speaker's Contact Info: tsibley(atsign)math.bu.edu
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