scholarly journals Uniformity in Association Schemes and Coherent Configurations: Cometric Q-Antipodal Schemes and Linked Systems

2010 ◽  
Author(s):  
Edwin van Dam ◽  
William Martin ◽  
Mikhail Muzychuk
Keyword(s):  
Association Schemes ◽  
Coherent Configurations

scholarly journals Recognizing Circulant Graphs in Polynomial Time: An Application of Association Schemes

10.37236/1570 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Mikhail E. Muzychuk ◽  
Gottfried Tinhofer
Keyword(s):  
Polynomial Time ◽  
Recognition Algorithm ◽  
Association Schemes ◽  
Circulant Graphs ◽  
Symmetry Properties ◽  
Coherent Configurations

In this paper we present a time-polynomial recognition algorithm for certain classes of circulant graphs. Our approach uses coherent configurations and Schur rings generated by circulant graphs for elucidating their symmetry properties and eventually finding a cyclic automorphism.

scholarly journals On some recent progress in the classification of $$(P\hbox { and }Q)$$-polynomial association schemes

2019 ◽  
Author(s):  
Alexander L. Gavrilyuk ◽  
Jack H. Koolen
Keyword(s):  
Symmetric Spaces ◽  
Recent Progress ◽  
Association Schemes ◽  
Compact Symmetric Spaces ◽  
Expository Paper

AbstractThe problem of classification of $$(P\hbox { and }Q)$$(PandQ)-polynomial association schemes, as a finite analogue of E. Cartan’s classification of compact symmetric spaces, was posed in the monograph “Association schemes” by E. Bannai and T. Ito in the early 1980s. In this expository paper, we report on some recent results towards its solution.

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