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Combining results on quadrics in projective geometries with an algebraic interplay between finite fields and Galois rings, we construct the first known family of partial difference sets with negative Latin square type parameters in nonelementary abelian groups, the groups Z 2k 4 × Z 4−4k 2 for all k when is odd and for all k < when is even. Similarly, we… (More)

- M Klin, Ch R Ucker, G R Ucker, G Tinhofer, Abcde Fghij Klmno, Mikhail Klin +3 others
- 1995

Let (G;) be a permutation group of degree n. Let V (G;) be the set of all square matrices of order n which commute with all permutation matrices corresponding to permutations from (G;): V (G;) is a matrix algebra which is called the centralizer algebra of (G;): In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent… (More)

This paper deals with graph invariants and stabilization procedures. We consider colored graphs and their automorphisms and we discuss the isomorphism problem for such graphs. Various global and local isomorphism invariants are introduced. We study canonical num-berings, invariant partitions, stable and equitable partitions and algorithms for stabilizing… (More)

- L Babel, I V Chuvaeva, M Klin, D V Pasechnik
- 1997

- Mikhail Klin
- 2015

- Mikhail Klin, Valery Liskovets, Reinhard Pp Oschel
- 1996

A method for the analytical enumeration of circulant graphs with p 2 vertices, p a prime, is proposed and described in detail. It is based on the use of S-rings and PP olya's enumeration technique. Two diierent approaches, \structural" and \multiplier", are developed and compared. As a result we get counting formulae and generating functions (by valency)… (More)

The paper concerns the automorphism groups of Cayley graphs over cyclic groups which have a rational spectrum (rational circulant graphs for short). With the aid of the techniques of Schur rings it is shown that the problem is equivalent to consider the automorphism groups of orthogonal group block structures of cyclic groups. Using this observation, the… (More)

We introduce a new notion of Siamese association scheme (the term " Siamese " can be traced to H.Kharaghani), and we investigate such objects. These are im-primitive schemes on v = (s 2 + 1)(s + 1) points having a unique closed subset of size s + 1 such that each connected basis graph is antipodal, distance-regular of valency s 2 and diameter 3, and is an… (More)

- Daniel Kalmanovich, Mikhail Klin
- 2012