Atlantic Graph Theory Seminar

Title: Computer constructions of distance-regular graphs with primitive automorphism groups

A graph is distance-regular if, for each vertex $v$ and each vertex $w$ at distance $i$ from $v$, the number of neighbours of $w$ at distances $i-1$, $i$ or $i+1$ from $v$ depends only on $i$, and not on the choice of $v$ or $w$.  These are highly-structured graphs with interesting structural and algebraic properties.  Many of the well-known examples have large symmetry groups.

The GAP computer algebra system contains libraries of primitive permutation groups (i.e. those which preserve no interesting equivalence relations).  With the assistance of my undergraduate research students, I have been analyzing these libraries with the ultimate aim of classifying the distance-regular graphs with such groups as automorphism groups.  In this talk, I will discuss the status of this work, a few surprises which came up along the way, and some (theoretical and computational) questions which remain open.

Meeting ID: 868 6149 9971

Passcode: 325258