scholarly journals Association schemes on 28 points as mergings of a half-homogeneous coherent configuration

2007 ◽  
Vol 28 (7) ◽  
pp. 1994-2025 ◽  
Author(s):  
M. Klin ◽  
M. Muzychuk ◽  
C. Pech ◽  
A. Woldar ◽  
P.-H. Zieschang
Keyword(s):  
Association Schemes ◽  
Coherent Configuration

scholarly journals Recognizing Circulant Graphs of Prime Order in Polynomial Time

10.37236/1363 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Mikhail E. Muzychuk ◽  
Gottfried Tinhofer
Keyword(s):  
Adjacency Matrix ◽  
Prime Order ◽  
Circulant Matrix ◽  
Recognition Algorithm ◽  
Association Schemes ◽  
Necessary Condition ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
Coherent Configuration ◽  
Schur Ring

A circulant graph $G$ of order $n$ is a Cayley graph over the cyclic group ${\bf Z}_n.$ Equivalently, $G$ is circulant iff its vertices can be ordered such that the corresponding adjacency matrix becomes a circulant matrix. To each circulant graph we may associate a coherent configuration ${\cal A}$ and, in particular, a Schur ring ${\cal S}$ isomorphic to ${\cal A}$. ${\cal A}$ can be associated without knowing $G$ to be circulant. If $n$ is prime, then by investigating the structure of ${\cal A}$ either we are able to find an appropriate ordering of the vertices proving that $G$ is circulant or we are able to prove that a certain necessary condition for $G$ being circulant is violated. The algorithm we propose in this paper is a recognition algorithm for cyclic association schemes. It runs in time polynomial in $n$.

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.

scholarly journals An Assmus–Mattson theorem for codes over commutative association schemes

2017 ◽  
Vol 86 (5) ◽  
pp. 1039-1062 ◽  
Author(s):  
John Vincent S. Morales ◽  
Hajime Tanaka
Keyword(s):  
Association Schemes

scholarly journals Width and dual width of subsets in polynomial association schemes

2003 ◽  
Vol 102 (2) ◽  
pp. 255-271 ◽  
Author(s):  
A.E. Brouwer ◽  
C.D. Godsil ◽  
J.H. Koolen ◽  
W.J. Martin
Keyword(s):  
Association Schemes
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