Designs, Codes and Cryptography

, Volume 34, Issue 2, pp 241–248

Algebraic Characterizations of Graph Regularity Conditions


DOI: 10.1007/s10623-004-4857-4

Cite this article as:
Curtin, B. Des Codes Crypt (2005) 34: 241. doi:10.1007/s10623-004-4857-4


It is well-known that a connected finite simple graph is regular if and only if the all-ones matrix spans an ideal of its adjacency algebra. We show that several other graph regularity conditions involving pairs and triples of vertices also have ideal theoretic characterizations in some appropriate algebras.

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of South FloridaTampaUSA