An algorithm for the classification of strongly regular graphs by means of lexically ordered adjacency matrices

Abstract

The concept of lexically ordered adjacency matrix of a graph is introduced and it is proved that every adjacency matrix is isomorphic to at least one lexically ordered adjacency matrix. An algorithm for the classification of strongly regular graphs is developed, where the property of lexical ordering is used as a means to reduce the number of generated adjacency matrices. We also describe other pruning methods that can be used.

Keywords:

• Strongly regular graph
• adjacency matrix
• lexical ordering
• classification algorithm