**PERSONAL DETAILS**

Name Klin Mikhail H. Date and place of birth July 5, 1946 Zitomir, the Ukraine Married (since 1983): Wife Inna Daughter: Hana (born in 1997)

B.A./B.Sc. M.Sc. 1964-69 Kiev State University Faculty of Mathematics and Mechanics Diploma with honour in Mathematics Name of advisor Prof. L. A. Kaluznin Title of thesis On some classes of permutation groups, preserving relations. Ph.D. 1973-75 Kiev State University Faculty of Mathematics and Mechanics Name of advisor Prof. L. A. Kaluznin (coadvisor L. L. Verbitskii) Title of thesis Investigation of relational algebras invariant under the action of certain classes of permutation groups.

**SELECTED SCIENTIFIC PUBLICATIONS **

1 a) Klin M.Ch., Pöschel R., Rosenbaum K.,

Angewandte Algebra für Mathematiker und Informatiker. Einführung in

gruppentheoretisch-kombinatorische Methoden (German).

(Applied algebra for mathematicians and information scientists. Introduction

to group-theoretical combinatorial methods.) VEB Deutscher Verlag der

Wissenschaften. Berlin, 208 pp., 1988.

1 b) Licence edition of 1 a). Fried. Vieweg & Sohn.

Braunschweig, 208 pp., 1988.

Review: MR, 1989, 89d:00018 (A.Schleiermacher).

1 c) Klin M.Ch., Pöschel R., Rosenbaum K.,

Algebra stosowana dla matematykow i informatikow.

Wydawnictwa Naukowo-Techniczne. Warszawa, 188 pp., 1992, 1994.

(Polish translation from 1a).

2. I.A.Faradzev, A.A.Ivanov, M.H.Klin, A.Woldar (editors)

Investigations in Algebraic Theory of Combinatorial Objects.

Kluwer Acad. Publ., 532 pp., 1994.

3. M.Klin, G.Tinhofer (editors).

A special issue of the journal MATCH,

"Algebraic Combinatorics in Mathematical Chemistry", v.40, 1999.

4. M.H.Klin, On the number of graphs for which a given permutation group

is the automorphism group (Russian).

Kibernetika(Kiev), #6, 131-137, 1970.

English translation: Kibernetika, 5, 892-870, 1973.

5. L.A.Kaluznin, M.H.Klin,

On certain maximal subgroups of symmetric and alternating groups (Russian).

Mat. Sb. (N.S.), 87(129), 91-121, 1972.

English transl.: Math. USSR-Sb., 16, 95-124, 1972.

6. Ja.Ju.Gol'fand, M.H.Klin, On k-homogeneous graphs (Russian).

Algorithmic Investigations in Combinatorics. Moscow, Nauka, 1978, 76-85.

7. L.A.Kaluznin, M.H.Klin, V.I.Sushchanskii, Exponentiation of permutation

groups. I (Russian). Izvestia VUZov, Mathematika, #8, 26-33, 1979.

English translation: Math. USSR-Izvestia VUZ, 25-33, 1979.

8. M.Ch.Klin, R.Pöschel, The isomorphism problem for circulant digraphs with *p*^{m} vertices.

Preprint. ZIMM, Berlin (1980), #34, 40 pp.

9. M.H.Klin, R.Pöschel, The König problem, the isomorphism problem
for cyclic graphs

and the method of Schur rings.

Algebraic Methods in Graph Theory, V.2, Budapest-Amsterdam. North Holland,

1981, 405-434.

10. A.A.Ivanov, M.H.Klin, S.V.Tsaranov, S.V.Shpektorov, On the problem of

the computation of subdegrees of transitive permutation groups (Russian), Uspekhi

matem. nauk, 38, #6, 115-116, 1983.

English translation: Russian Math. Surveys, 38, #6, 123-124, 1983.

11. Ja.Ju.Gol'fand, M.H.Klin, Amorphic cellular rings. I (Russian).
In: M.H.Klin, I.A.Faradzev (editors)

Investigations in algebraic theory of
combinatorial objects. Proceedings of a seminar.

Moscow, VNIISI, 187 pp, 1985,
32-38.

English translation: I.A.Faradzev e.a. (eds.), Investigations in Algebraic Theory of

Combinatorial Objects. Kluwer Acad.Publ., 1994, 167-187.

12. A.E.Brouwer, A.V.Ivanov, M.H.Klin, Some new strongly regular graphs.

Combinatorica, 9, 339-344, 1989.

13. M.H.Klin, S.S.Tratch, N.S.Zefirov, 2D-configurations and clique-cyclic

orientations of graphs *L*(*K*_{p}). Reports in Molecular Theory, 1, 149-163, 1990.

14. M.H.Klin, S.S.Tratch, N.S.Zefirov, Group-theoretical approach to the investigation

of reaction graphs for highly degenerate rearrangements of chemical compounds. I.

Criterion of the connectivity of the graph. J. Math. Chem. 7, 135-151, 1991.

15. I.A.Faradzev, M.H.Klin, Computer package for computations with coherent

configurations. Proc. of the 1991 Intern. Symp. on Symb. and Algebr. Computations,

ISSAC' 91 (Bonn, July 15-17, 1991), ACM Press, 219-223.

16. A.W.M.Dress, M.H.Klin, M.E.Muzichuk, On *p*-configurations with few slopes

in the affine plane over *F*_{p} and a theorem of W.Burnside's.

Bayreuther Math. Schriften, 40, 7-19, 1992.

18. M.Klin, A.Munemasa, M.Muzychuk, P.-H.Zieschang,

Directed strongly regular graphs via coherent (cellular) algebras.

Preprint. Kyushu - MPS - 1997 - 12,

Kyushu University, Fukuoka, Japan, 1997, 57 pp.

(Revised version submitted to Linear Algebra and its Applications.)

19. M.Muzychuk, M.Klin, On graphs with three eigenvalues.

Discrete Mathematics, 189, 191-207, 1998.

20. A.Betten, M.Klin, R.Laue, A.Wasserman,

Graphical designs via Polynomial Kramer-Mesner matrices.

Discrete Mathematics, 197-198, 83-109, 1999.

21. G.Jones, M.Klin, F.Lazebnik,

Automorphic subsets of the *n*-dimensional cube.

Beiträge zur Algebra und Geometrie, 41, No.2, 303-323, 2000.

22. M.Muzychuk, M.Klin, R.Pöschel.

The isomoprhism problem for circulant graphs via Schur ring theory.

DIMACS Series in Discrete Mathematics 56, 241-264, 2001.

23. P.J.Cameron, M.Giudici, G.A.Jones, W.M.Kantor, M.H.Klin,
D.Marusic,
L.A.Nowitz. Transitive permutation groups without semiregular subgroups.

To appear in the Journal of the London Mathematical Society.

24. G.Jones, M.Klin, Y.Moshe. Primitivity of permutation groups,
coherent algebras and matrices.

Journal of Combinatorial Theory. Series A 98, 210-217, 2002.

__A SHORT SYNOPSIS OF RESEARCH__

Applications of Burnside rings in combinatorial enumeration: [2], [4], [10].

A new approach to the investigation of
maximal and close to maximal subgroups of symmetric groups, which
is based on the use of certain Galois correspondences between finite
permutation groups and relational algebras: [1], [2], [5], [7].

Theory of finite permutation groups,
in particular counting of subdegrees of transitive permutation
groups, properties of the k-closure of a permutation group, the
investigation of primitive representations of simple groups, and new
elementary proofs of some classical results which go back to Burnside,
Schur and Wielandt: [1], [2], [5], [7], [10], [16].

New developments of the methods of the theory of Schur rings
for the identification of circulant graphs and the description of their
symmetry: [2], [3], [8], [9], [22].

Investigation of k-homogeneous and k-isoregular graphs, complete
characterization of the absolutely homogeneous graphs: [1], [6].

Theory of the association schemes, in particular
introduction and characterization
of the amorphic association schemes and Frobenius primitive
association schemes: [2], [11], [24].

A novel approach to the use of the methods of computer algebra
in algebraic combinatorics, elaboration of a computer package COCO
for the computations with coherent configurations: [2], [15].

Discovery of new infinite series and sporadic examples of new
strongly regular graphs with certain exceptional properties: [2], [12],
[15].

Investigation of directed and undirected graphs with three eigenvalues,
new techniques for the construction of such graphs: [18], [19].

Mathematical chemistry, in particular new applications of the methods
of algebraic combinatorics and discrete geometry,
elaboration of a new approach for the investigation
of reaction graphs of highly degenerate rearrangements
of chemical compounds: [3],
[13], [14].

Elaboration of a more general polynomial version of
the Kramer-Mesner matrices for the construction of combinatorial *t*-designs: [20].

Introduction of amorphic subsets of the *n*-dimensional cube
(a promising generalization of classical binary linear codes): [21].

Putting, long standing promotion and investigation of the so-called
Marusic, Jordan and Klin conjecture
about 2-closed transitive permutation groups without semiregular subgroups: [23].

(b) __Selected articles to be published __

1. On the analytical enumeration of circulant graphs.
Jointly with V.A.Liskovets and R.Pöschel (in preparation).

2. Authomorphism groups of *p*^{m}-vertex circulant graphs, *p* - an odd prime. Jointly with R.Pöschel (in preparation).

3. Enumeration of small partial difference sets.
Jointly with A.Heinze (in preparation).

4. Partial difference sets in known and new strongly regular graphs
on 100 vertices.

Jointly with L.Joergensen (in preparation).

5. Circulant graphs via S-ring theory. I. Fundamental concepts.

Jointly with M.Muzychuk and A.Woldar (in preparation).

6. Chromatic polynomials and association schemes:

an interplay between two well-known approaches in algebraic
graph theory.

Jointly with Ch. Pech (in preparation).

8. Normally regular digraphs and association schemes with three classes.

Jointly with L.Lörgensen, G.Jones and S.Y.Song (in preparation).

9. Some implications on amorphic association schemes.

Jointly with E.van Dam and M.Muzychuk (in preparation).

10. Coherent algebras and association schemes. A gentle
introduction. Jointly with G.Tinhofer and A.Woldar (in preparation).

11. Enumeration of vertex transitive association schemes
and graphs. Jointly with F.Fiedler and C.Pech (in preparation).

12. On 4-isoregular graphs. II.
4-isoregularity of the McLaughlin graph.

Jointly with A.Woldar (paper in progress).

13. A strongly regular graph on 120 vertices via seven-point Fano plane.

Jointly with G.Jones and E.K.Lloyd (paper in progress).

14. Lattice of 2-closed overgroups of the exponentiation
in symmetric group *S*_{2n}.

Jointly with M.Muzychuk and V.A.Ustimenko (paper in progress).

15. Group-theoretical approach to the investigation of reaction graphs

of highly degenerate
rearrangements of chemical compounds. III. Automorphism groups.

Jointly with M.Muzychuk (paper in progress).

(a) __Selected research projects in progress __

1. Introduction to algebraic combinatorics (book in English).

Jointly with R.Pöschel (Dresden) and A.Woldar (Villanova), 1996-2003.

2. Graph-theoretical approach to chemical crystallography.

Jointly with J.Bernstein (Beer-Sheva) and G.Jones (Southampton), 1998-2004.

3. Coherent algebras, association schemes, Schur rings and symmetry of graphs.

A collection of scientific papers. (M.Klin and A.Woldar, editors.), 1998-2002.

4. Strongly regular graphs with 4-condition.

Jointly with M.Meszka (Krakow), S.Reichard (Newark)
and A.Rosa (Hamilton), 2001-2003.

(a) __Links to research collaborators__

Norman Biggs

Andries Brouwer

Peter Cameron

Edwin van Dam

Aiso Heinze

Sasha Ivanov

Reinhard Laue

Felix Lazebnik

Akihiro Munemasa

Mikhail Muzychuk

Christian Pech

Reinhard Pöschel

Sven Reichard

Gottfried Tinhofer

Andy Woldar