Publications, etc.
Published Research Papers:
 On Some Infinite Series of Maximal Subgroups of Alternating
Groups,
Voprosi Teorii Grypp i Gomologicheskoi Algebri,
1, 125136, 1977. MR 81a:20006.
 On the number of colorings of graphs with fixed numbers of
vertices and edges,
Congressus Numerantium , 65 (1988), 6988. MR
90j:05068.
 On the greatest number of 2 and 3 colorings of a
(v,e)graph,
Journal of Graph Theory, Vol. 13, No. 2, 203214
(1989). MR 90d:05099.
[pdf]
 New upper bounds for the greatest number of proper colorings
of a $(v,e)$graph,
Journal of Graph Theory, Vol. 14, No. 1, 2529
(1990). MR 91b:05079.
[pdf]
 (joint work with G. Ebert, J. Hemmeter and A. J. Woldar),
On the irregularity strength of some graphs,
Congressus Numerantium , 71 (1990), 3952. MR
91b:05169.
[pdf]
 Some corollaries of a theorem of Whitney on the chromatic
polynomial,
Discrete Mathematics , 87 (1991) 5364. MR
91m:05084.
[pdf]
 On the number of maximal independent sets in some
$(v,e)$graphs,
Proceedings of the Sixth International Conference on the
Theory and Applications of Graphs ,
vol. 2, Willey, Inc., 1991, 743752. MR 93c:05065.
[pdf]
 (joint work with G. Ebert, J. Hemmeter and A. J. Woldar),
On the number of irregular assignments on a graph ,
Discrete Mathematics , 93 (1991) 131142. MR
93b:05147.
[pdf]
 (joint work with D.K. Garnick and Y.H.H. Kwong),
Extremal Graphs without ThreeCycles or FourCycles,
Journal of Graph Theory , Vol.17, No. 5, 633645
(1993). MR 94j:05068.
[pdf]
[ps]
 (joint work with V.A. Ustimenko),
Some Algebraic Constructions of Dense Graphs of Large Girth and
of Large Size,
in ``Expanding Graphs", edited by J. Friedman, DIMACS Series in
Discrete Mathematics and
Theoretical Computer Science, Volume 10, AMS, (1993), 7593. MR
1 235 569.
[pdf]
 (joint work with V.A. Ustimenko),
New examples of graphs without small cycles and of large size,
Europ. J. Combinatorics , 14, no. 5, (1993),
445460. MR 94j:05071.
[pdf]
[ps]
 (joint work with R.D. Baker, J. Bonin and E. Shustin),
On the number of nowhere zero points of linear mappings,
Combinatorica , 14, (2) (1994) 149157. MR
95k:11160.
[pdf]
[ps]
 (joint work with V. A. Ustimenko and A. J. Woldar),
New Constructions of Bipartite Graphs on $m,n$ vertices, with
Many Edges, and without Small Cycles,
Journal of Combinatorial Theory , Series B, vol.61,
No. 1, 1994, 111117. MR 95c:05125.
[pdf]
[ps]
 (joint work with V. A. Ustimenko and A. J. Woldar),
Properties of Certain Families of $2k$Cycle Free Graphs,
Journal of Combinatorial Theory , Series (B), 60, No.
2, (1994), 293298. MR 95a:05050.
[pdf]
[ps]
 (joint work with G. Fiorini),
On a bound for the maximum number of $C_8's$ in a 4cycle free
bipartite graph
Congressus Numerantium , 99 (1994), 191197. MR
95d:05076.
[pdf]
See also:
[pdf] and
[ps]
 (joint work with V.A. Ustimenko),
Explicit construction of graphs with arbitrary large girth and
of large size,
Discrete Applied Mathematics , 60 (1995) 275284. MR
96e:05088
[pdf]
[ps]
 (joint work with D.K. Garnick and Y.H.H. Kwong),
Algorithmic Search For Extremal Graphs of Girth Five ,
Proceedings of the Seventh Quadrennial International
Conference
on the Theory and Applications of Graphs, WMU, 1992,
Volume 2, Y. Alavi and A. Schwenk Eds.,
John Wiley and Sons, 1995, New York, 697709. MR 97c:05144. [pdf]
[ps]
 (joint work with V.A. Ustimenko and A.J. Woldar),
A New Series of Dense Graphs of High Girth,
Bulletin of the AMS, Volume 32, Number 1, (1995)
7379. MR 95f:05066.
[pdf]
[ps]
 (joint work with Z. Füredi, Á. Seress, V. A. Ustimenko, and
A. J. Woldar),
Graphs of Prescribed Girth and BiDegree,
Journal of Combinatorial Theory, Ser. B Vol. 64, No.
2, (1995) 228239. MR 96i:05143.
[pdf]
[ps]
 (joint work with V.A. Ustimenko and A.J. Woldar),
A Characterization of the Components of the graphs $D(k,q)$,
Discrete Mathematics, 157 (1996) 271283. MR
97h:05150.
[pdf]
 (joint work with V.A. Ustimenko and A.J. Woldar),
New upper bounds on the order of cages,
Electronic Journal of Combinatorics, Volume 14, R13,
(1997), 111. MR 98e:05066.
[pdf]
[ps]
 (joint work with P. Wang),
On the Structure of Extremal Graphs of High Girth,
Journal of Graph Theory, 26, (1997), 147153. MR
99d:05026
[pdf]
[ps]
 (joint work with W. Li and R. Martin),
Random walks on rooted trees,
The Bulletin of the ICA, Volume 22, (1998), 5966.
MR 2001b:05151.
[pdf]
[ps]
 (joint work with G. Fiorini),
An Extremal Characterization of the Incidence Graphs of
Projective Planes,
Applicandae Matematicae, 52: (1998), 257260. MR
99i: 05109
[pdf] [ps]
For an extended version of this paper, see
[pdf]
[ps]
 (joint work with V.A. Ustimenko and A.J. Woldar),
Polarities and $2k$cyclefree graphs,
Discrete Mathematics, 197/198, (1999), 503513. MR
99i: 05123.
[pdf]
[ps]
 (joint work with M.H. Klin and G. Jones),
Introduction to the Theory of Automorphic Subsets of the
$n$dimensional Cube,
Beiträge zur Algebra und Geometrie,
(Contributions to Algebra and Geometry,)
Volume 41 (2000), No.2, 303323. MR 2001k: 05108.
[pdf]
[ps]
 (joint work with A.J. Woldar),
New lower bounds on multicolored Ramsey numbers $r_k(C_4)$.
Journal of Combinatorial Theory, Ser. B 79, (2000),
172176. MR 2001b: 05151.
[pdf]
[ps]
 (joint work with A.J. Woldar),
General properties of some families of graphs defined by systems
of equations.
Journal of Graph Theory, 38, (2001), 6586. MR 2002k:
05108.
[pdf]
[ps]
 (joint work with D. Mubayi),
New lower bounds for Ramsey numbers of graphs and hypergraphs.
Advances in Applied Mathematics, Vol. 28, No. 3/4,
(2002), 544559. MR 2003d: 05144.
[pdf]
[ps]
 (joint work with R. Viglione),
An infinite series of regular edge but not vertextransitive
graphs.
Journal of Graph Theory, 41, (2002), 249258. MR 1
936 942.
[pdf]
[ps]
 (joint work with J. Verstraëte),
On Hypergraphs of Girth Five.
Electronic Journal of Combinatorics, Volume 10, R25,
(2003), 115.
[pdf]
[ps]
 (joint work with A. Thomason),
Orthomorphisms and the Construction of Projective Planes.
Mathematics of Computation, Volume 73, Number 247,
(2004), 15471557.
[pdf]
[ps]
 (joint work with R. Viglione),
On the connectivity of certain graphs of high girth.
Discrete Mathematics, 277, (2004), 309319.
[pdf]
[ps]
 (joint work with V. Dmytrenko and R. Viglione),
An Isomorphism Criterion for Monomial Graphs. Journal of
Graph Theory, 48, (2005), 322328.
[pdf]
 (joint work with R.S. Coulter and M. Henderson),
On certain combinatorial diophantine equations and their
connection to Pythegorean numbers.
Acta Arithmetica, 122, (2006), 395406.
[pdf]
[ps]
 (with V. Dmytrenko and J. Williford),
On monomial graphs of girth eight.
Finite Fields and Their Applications, 13, (2007),
828842.
[pdf]
Here are comments on this paper prepared by Brian Kronenthal:
[pdf]
 (with O. Pikhurko and A. J. Woldar),
Maximum Number of Colorings of (2k,k^2)graphs.
Journal of Graph Theory, Volume 56, Issue 2, (2007),
135148.
[pdf]
 (with B. Cuckler),
Irregularity Strength of Dense Graphs.
Journal of Graph Theory, Volume 58, Issue 4, (2008),
299313.
[pdf]
 (with S. De Winter and J. Verstraete),
An Extremal Characterization of Projective Planes.
Electronic Journal of Combinatorics, Volume 15(1),
R143, (2008), 113.
[pdf]
 (with K. E. Mellinger and O. Vega),
On the number of kgons in finite projective planes.
Note di Matematica, 29 (2009), suppl. no. 1, 135 
152.
[pdf]
 (with S.N. Tofts),
An Extremal Property of Turan's Graphs.
The Electronic Journal of Combinatorics, Volume 17(1),
R170, (2010), 111.
[pdf]
 (with R.S. Coulter),
On the Classification of Planar Monomials over Fields of Square
Order.
Finite Fields and Their Applications, Volume 18, Issue
2, (2012), 316336.
[pdf]
43. (with K.E. Mellinger and O. Vega),
Embedding
cycles in finite planes.
The Electronic
Journal of Combinatorics, Volume 20, Issue 3, P24 (2013),
117.
[pdf]
44. (with S.M. Cioaba and Weiqiang Li),
On the Spectrum of
Wenger Graphs.
Journal of
Combinatorial Theory, Ser. B 107: (2014), 132139. [pdf]
45. (with A. Kodess),
Connectivity of Some Algebraically Defined
Digraphs.
The Electronic Journal of Combinatorics 22(3) (2015), #P3.27, 111. [pdf]
46. (with A. Thomason and Y. Wang),
On Some Cycles in Wenger Graphs.
To appear in Acta Math. Appl. Sin. Engl.
[pdf]
47. (with B. Kronenthal),
On the uniqueness of some girth eight algebraically defined graphs.
Applied Discrete Mathematics 206 (2016) 188194. [pdf]
48. (with A. Kodess, S. Smith and J. Sporre),
Diameter of some monomial digraphs.
Contemporary Developments in Finite Fields and Applications,
A. Canteaut, G. Effinger, S. Huczynska, D. Panario, L. Storme Eds.,
World Scientific, Singapur, 2016, 160177. [pdf]
49. (with Xiangdong Hou and Stephen D. Lappano),
Proof of a Conjecture on Monomial Graphs.
Finite Fields and Their Applications, Volume 43 (2017), pp. 4268. [pdf]
50. (with Shuying Sun and Ye Wang),
Some Families of Graphs, Hypergraphs and Digraphs
Defined by Systems of Equations:
A Survey.
Lecture Notes of Seminario Interdisciplinare di Matematica , Vol. 14 (2017), pp. 105–142. [pdf]
51. (with A. Kodess),
A note on the Isomorphism Problem for Monomial Digraphs,
Journal of Interconnection Networks, 17 (2017) 1741006 (12 pages).
Dedicated to IWONT 2016 conference in honor to the memory of
Mirka Miller (1949  2016). [pdf],
Published book:
1. (with O. Byer and D.L. Smeltzer),
Methods for Euclidean
Geometry.
Mathematical Association of
America, Inc., 2010, 1461.
For selected chapters click here.
Published expository and teachingoriented papers:
 Affine and Projective Planes,
Y Sviti Matematiki, 6, 91107, 1975
 Systems of Distinct Representatives,
Y Sviti Matematiki, 7, 5063, 1976
 On a Method in Algebra and Geometry,
The AMATYC Reviews, v. 12, No. 1 (1990), 7072, and
v. 12, No. 2 (1991) 4748
[pdf]
[ps]
 (with J. Hemmeter and A. J. Woldar),
Translated from Russian and edited a survey article for a volume
on
Algebraic Combinatorics for Kluwer Acad. Publ., (1990) (218
pages)
 On Systems of Linear Diophantine Equations,
The Mathematics Magazine, vol. 69, no. 4, October
1996, 261266.
[pdf]
[ps]
 (with M.H. Klin, G. Pöschel, V.I. Suschansky, V.A. Ustimenko,
V.I. Vyshensky),
Lev Arkad'evich Kaluznin
Applicandae Matematicae, 52:(1998) 518 MR 99m:
01091.
A shorter version of this article can be found here:
[html]
 (with K.E. Mellinger),
Some Advice for Graduating PhD Students. FOCUS,
Volume 26, Issue 6, 1415, 2006.
[pdf file
from the journal] or
[pdf file; preprint(shorter)]
8. Surprises. The Mathematics
Magazine, Vol.
87, No. 3, June 2014, 212221.
[pdf]
9. (with B.
Kronenthal)
When
can you factor a quadratic form?
The
Mathematics Magazine, Vol. 87, No.
1, February 2014, 2536.
[pdf]
10. Herbert S. Wilf
(19312012)
in the
Notices of the AMS Volume 62, Number 4, April 2015,
346360. [pdf]
11. Patricia Miller Overdeer: An Educator
and Alumna.
Reckonings, Newsletter of the Department of Mathematical Sciences,
Summer 2014 and 2015, 2223.
[pdf]
Published Problems:
 A problem on Congruences for the binomial
coefficients,
Matematika v shkole,
1, 1974
 (with Y.I. Pilipenko),
Problem # E3036,
The American Mathematical
Monthly, Vol 91, No. 2, 1984
 (with D.P. Bellamy and J.C. Lagarias),
Problem # E10656: On the number of positive
integer solutions of $tan n > n$,
The American Mathematical
Monthly, Vol. 105, No. 4, 1998. [pdf]
[ps]
 (with D.P. Bellamy),
Problem # E10729 : On solutions of a class of
differential equations,
The American Mathematical
Monthly, Vol. 106, No. 4, 1999
[pdf]
[ps]
 (with V. Dmytrenko),
Problem # Q949: An Identity for Binomial
Coefficients,
Mathematics Magazine,
Vol. 78, No. 2, 2005, 159; 164.
[pdf]
[ps]
Submitted manuscripts:

Chapter for The Handbook on Graph Polynomials:
The Maximum Number of Colorings of Graphs of Given Order and Size (preliminary version, 15 pages):
[pdf]
 (with S. DeWinter, R. Coulter and A. Kodess),
A result on polynomials inspired by graph theory:[pdf]
 (with B.G. Kronenthal and J. Williford),
On the uniqueness of some girth eight
algebraically defined graphs, Part II [pdf]
 (with S.M. Cioba and S. Sun),
Spectral and Combinatorial Properties of Some Algebraically Defined Graphs[pdf]
Research Reports:
 (joint work with D.K. Garnick and Y.H.H. Kwong),
Graphs without TreeCycles or FourCycles for
each order from 25 to 200
Research. Rep.
912, Dept. of C.S., Bowdoin College,Brunswick, ME, 1991.
(See references #9 and #17 in Published Research
Papers section.)
 (joint work with V.A. Ustimenko and A.J. Woldar),
A New Series of Dense Graphs of Large Girth ,
RUTCOR Research Report,
RRR 9993, December 1993 [ps
file can be found here]
 (joint work with M.H. Klin and G. Jones),
Introduction to the Theory of Automorphic
Subsets of the $n$dimensional Cube,
Preprint Series University of
Southampton, No. 309, August 1998
 (joint work with A.J. Woldar),
General properties of some families of
algebraically defined graphs,
Research Report,
University of Delaware, May, 1999.
Theses:
 Arrangements of Some Geometrical Groups in Symmetric
Groups,
Master's Thesis, University of Kiev, (1975)
 Some Extremal Problems for Graphs with Fixed Numbers
of Vertices and Edges,
Ph.D. Thesis, University of Pennsylvania, (1987)
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