Triple intersection numbers for the Paley graphs

TL;DR

This paper establishes a precise bound on the triple intersection numbers in Paley graphs, demonstrating that for graphs larger than order 25, any three vertices share at least one common neighbor.

Contribution

It provides a tight bound for triple intersection numbers in Paley graphs and proves the existence of a common neighbor for any three vertices in sufficiently large graphs.

Findings

Any three vertices in Paley graphs of order > 25 have a common neighbor.

The paper derives a tight bound for triple intersection numbers.

Paley graphs exhibit specific intersection properties for large orders.

Abstract

We give a tight bound for the triple intersection numbers of Paley graphs. In particular, we show that any three vertices have a common neighbor in Paley graphs of order larger than 25.