This project attempts to find all of the Moore Graphs with girth 5. According to Wikipedia: The Hoffman–Singleton theorem states that any Moore graph with girth 5 must have degree 2, 3, 7, or 57. The Moore graphs are:

  • The complete graphs K_n on n > 2 nodes. (diameter 1, girth 3, degree n-1, order n)
  • The odd cycles C_{2n+1} . (diameter n, girth 2n+1, degree 2, order 2n+1)
  • The Petersen graph. (diameter 2, girth 5, degree 3, order 10)
  • The Hoffman–Singleton graph. (diameter 2, girth 5, degree 7, order 50)
  • A hypothetical graph of diameter 2, girth 5, degree 57 and order 3250; it is currently unknown whether such a graph exists. Unlike all other Moore graphs, Higman proved that the unknown Moore graph cannot be vertex-transitive.

This code should be pretty easy to compile as there are no requirements on any libraries outside of the standard right now. I was going to accelerate this with cuda and omp, but a factor of 100 increase in speed wouldn’t really help you with the 57 degree graph and would be unnoticeable with the 7 or 3 as they are already extremely fast. You will probably have to change the CC variable in the makefile to fit your system and you will need a c++ compiler that is modern enough to support C++11 features.

Github link