6 research outputs found
On highly regular strongly regular graphs
In this paper we unify several existing regularity conditions for graphs,
including strong regularity, -isoregularity, and the -vertex condition.
We develop an algebraic composition/decomposition theory of regularity
conditions. Using our theoretical results we show that a family of non rank 3
graphs known to satisfy the -vertex condition fulfills an even stronger
condition, -regularity (the notion is defined in the text). Derived from
this family we obtain a new infinite family of non rank strongly regular
graphs satisfying the -vertex condition. This strengthens and generalizes
previous results by Reichard.Comment: 29 page
Permutation group approach to association schemes
AbstractWe survey the modern theory of schemes (coherent configurations). The main attention is paid to the schurity problem and the separability problem. Several applications of schemes to constructing polynomial-time algorithms, in particular, graph isomorphism tests, are discussed