The Shrikhande graph

A Window on Discrete Mathematics

This book is currently in press in the London Mathematical Society Lecture Note Series, from Cambridge University Press; ISBN 9781009709101 (hardback), 9781009709088 (paperback).

Here I will keep items related to the book or its subject, the celebrated Shrikhande graph.

The authors

The authors

Recent results about the Shrikhande graph

  1. The design spectrum of a simple graph G is the set of positive integers n for which the edge set of the complete graph on n vertices can be decomposed into copies of G. Tony Forbes and Carrie Rutherford have shown that the design spectrum of the Shrikhande graph consists of all integers congruent to 1 (mod 96). This paper is on the arXiv, 2505.00859.
  2. Alexander Ivanov has written an interesting account of the Shrikhande graph inside the Higman–Sims (or Mesner) graph on 100 vertices.
  3. Peter Cameron has shown that there is a triality associated with the Shrikhande graph: take three pairwise dijoint copies of the graph, then it is possible to put between any two the bipartite Dyck graph in such a way that the resulting graph has automorphism group permuting the three copies as the symmetric group, and inducing the full automorphism group of the Shrikhande graph on each copy.