Triple intersection numbers in distance-regular graphs
Presented by Mr. Aleksandar JURISIC
Type: Oral presentation
Track: Representations of Graphs
A graph is said to be $t$-tuple regular if, for any set $S$ of vertices with $|S|\le t$, the number of common neighbours of $S$ depends only on the isomorhism type of the induced subgraph on $S$. It follows immediately that a graph is 1-tuple regular iff it is regular, and it is 2-tuple regular iff it is strongly regular. Cameron and Van Lint studied 3-tuple regular graphs, and they characterized them with strongly regular graphs that have strongly regular subconstituents. We generalize their study to distance-regular graphs and investigate triple intersection numbers. Some of the results in this talk are a joint work with Paul Terwilliger and/or Jack Koolen.