Algebraic Characterizations of Graph Regularity Conditions
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- Curtin, B. Des Codes Crypt (2005) 34: 241. doi:10.1007/s10623-004-4857-4
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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.