On Classifying Finite Edge Colored Graphs with Doubly Transitive Automorphism Groups

Thomas Q. Sibley

St. John's University

Febrary 24,
refreshments at 3:45pm


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(at-sign)math.bu.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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