Disconnected vertex sets and equidistant code pairs.
Embedding arbitrary graphs into strongly regular and distance-regular graphs.
Extension of strongly regular graphs.
Finding the automorphism group of a circulant association scheme in polynomial time.
Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency property.
Introduction to association schemes.
Isometry classes of generalized associahedra.
Lattices and association schemes : a unimodular example without roots in dimension 28
Some interesting lattices can be constructed using association schemes. We illustrate this by a unimodular lattice without roots of dimension 28 which admits as its automorphism group.
Leonard pairs from the equitable basis of .
Loop characters
A survey of the basic results of loop characters is given on the lines of the treatment of the author and J.D.H. Smith for characters of quasigroups, including some recent deveploments. One of the successes of the theory has been its suggestive influence on the theory of association schemes, group representations and the theory of the group determinant, and selected results arising are described. A section is devoted to an explanation of how the tool of loop characters has not yet been as startlingly...
Metric coset schemes revisited
An Abelian scheme corresponds to a special instance of what is usually named a Schur-ring. After the needed results have been quoted on additive codes in Abelian schemes and their duals, coset configurations, coset schemes, metric schemes and distance regular graphs, partition designs and completely regular codes, we give alternative proofs of some of those results. In this way we obtain a construction of metric Abelian schemes and an algorithm to compute their intersection matrices.
Metrically regular square of metrically regular bigraphs. I
Metrically regular square of metrically regular bigraphs. II.
Metrically regular bigraphs the square of which are metrically regular graphs are investigated in the case of graphs with 6 distinct eigenvalues (these eigenvalues can have variuos multiplicities).
Metrically regular square of metrically regular bipartite graphs of diameter
The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter see [7] and [8].
Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)
Modular invariance property of association schemes is recalled in connection with our joint work with François Jaeger. Then we survey codes over discussing how codes, through their (various kinds of) weight enumerators, are related to (various kinds of) modular forms through polynomial invariants of certain finite group actions and theta series. Recently, not only codes over an arbitrary finite field but also codes over finite rings and finite abelian groups are considered and have been studied...
New prolific constructions of strongly regular graphs.
New regular partial difference sets and strongly regular graphs with parameters and .
New upper bounds for the size of permutation codes via linear programming.
Non-isomorphic graphs with cospectral symmetric powers.
Odd-vertex-degree trees maximizing Wiener index