- On Some Infinite Series of Maximal Subgroups of Alternating Groups,

*Voprosi**Teorii Grypp i Gomologicheskoi Algebri,*

1, 125–136, 1977. (In Russian) MR 81a:20006. - On the number of colorings of graphs with fixed numbers of vertices and edges,

*Congressus**Numerantium ,*65 (1988), 69–88. 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, 203–214 (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, 25–29 (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), 39–52. MR 91b:05169. [pdf] - Some corollaries of a theorem of Whitney on the chromatic polynomial,

*Discrete Mathematics ,*87 (1991) 53–64. 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, 743–752. 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) 131–142. MR 93b:05147. [pdf] - (joint work with D.K. Garnick and Y.H.H. Kwong),

Extremal Graphs without Three-Cycles or Four-Cycles,

*Journal of Graph Theory ,*Vol.17, No. 5, 633–645 (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), 75–93. 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), 445–460. 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* - (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, 111–117. 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), 293–298. MR 95a:05050. [pdf] [ps] - (joint work with G. Fiorini),

On a bound for the maximum number of $C_8’s$ in a 4–cycle free bipartite graph

*Congressus**Numerantium ,*99 (1994), 191–197. 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) 275–284. 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*WMU, 1992, Volume 2, Y. Alavi and A. Schwenk Eds.,

on the Theory and Applications of Graphs,

John Wiley and Sons, 1995, New York, 697-709. 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) 73–79. MR 95f:05066. [pdf] [ps] - (joint work with Z. Furedi, A. Seress, V. A. Ustimenko, and A. J. Woldar),

Graphs of Prescribed Girth and Bi–Degree,

*Journal of Combinatorial Theory,*Ser. B Vol. 64, No. 2, (1995) 228–239. 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) 271–283. 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), 1–11. 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), 147–153. 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), 59–66. MR 2001b:05151. [pdf] [ps] - (joint work with G. Fiorini),

An Extremal Characterization of the Incidence Graphs of Projective Planes,

*Applicandae**Matematicae,*52: (1998), 257–260. 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 $2k$-cycle-free graphs,

*Discrete Mathematics,*197/198, (1999), 503–513. 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,

*Beitrage**zur Algebra und Geometrie, (Contributions to Algebra and Geometry,)*

Volume 41 (2000), No.2, 303–323. 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), 172–176. 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), 65–86. 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), 544–559. MR 2003d: 05144. [pdf] [ps] - (joint work with R. Viglione),

An infinite series of regular edge- but not vertex-transitive graphs.

*Journal of Graph Theory,*41, (2002), 249–258. MR 1 936 942. [pdf] [ps] - (joint work with J. Verstraete),

On Hypergraphs of Girth Five.

*Electronic Journal of Combinatorics,*Volume 10, R25, (2003), 1–15. [pdf] [ps] - (joint work with A. Thomason),

Orthomorphisms and the Construction of Projective Planes.

*Mathematics of Computation,*Volume 73, Number 247, (2004), 1547–1557. [pdf] [ps] - (joint work with R. Viglione),

On the connectivity of certain graphs of high girth.

*Discrete Mathematics,*277, (2004), 309–319. [pdf] [ps] - (joint work with V. Dmytrenko and R. Viglione),

An Isomorphism Criterion for Monomial Graphs.*Journal of Graph Theory,*48, (2005), 322–328. [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), 395–406. [pdf] [ps] - (with V. Dmytrenko and J. Williford),

On monomial graphs of girth eight.

*Finite Fields and Their Applications,*13, (2007), 828–842. [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), 135–148. [pdf] - (with B. Cuckler),

Irregularity Strength of Dense Graphs.

*Journal of Graph Theory,*Volume 58, Issue 4, (2008), 299–313. [pdf] - (with S. De Winter and J. Verstraete),

An Extremal Characterization of Projective Planes.

*Electronic Journal of Combinatorics,*Volume 15(1), R143, (2008), 1–13. [pdf] - (with K. E. Mellinger and O. Vega),

On the number of k-gons 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), 1–11. [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), 316–336. [pdf] - (with K.E. Mellinger and O. Vega),

Embedding cycles in finite planes.Volume 20, Issue 3, P24 (2013), 1–17. [pdf]

The Electronic Journal of Combinatorics, - (with S.M. Cioaba and Weiqiang Li),

On the Spectrum of Wenger Graphs.

*Journal of Combinatorial Theory,*Ser. B 107: (2014), 132–139. [pdf] - (with A. Kodess),

Connectivity of Some Algebraically Defined Digraphs.

*The Electronic Journal of Combinatorics*22(3) (2015), #P3.27, 1–11. [pdf] - (with A. Thomason and Y. Wang),

On Some Cycles in Wenger Graphs.

*Acta Math. Appl. Sin. Engl.,*vol. 36, (2020), 492–502. [pdf] - (with B. Kronenthal),

On the uniqueness of some girth eight algebraically defined graphs.

*Discrete Applied Mathematics*206 (2016) 188–194. [pdf] - (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, 160–177. [pdf] - (with Xiang-dong Hou and Stephen D. Lappano),Proof of a Conjecture on Monomial Graphs.

*Finite Fields and Their Applications,*Volume 43 (2017), pp. 42–68. [pdf] - (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] - (with A. Kodess),

A note on the Isomorphism Problem for Monomial Digraphs,

*Journal of Interconnection Networks*, 17 (2017) 1741006 (12 pages).

IWONT 2016 Conference in honor to the memory of

Mirka Miller (1949 – 2016). [pdf] - (with S.M. Cioaba and Shuying Sun),

Spectral and Combinatorial Properties of Some Algebraically Defined Graphs

*The Electronic Journal of Combinatorics*25(4) (2018), #P4.60,[pdf] - (with B.G. Kronenthal and J. Williford),

On the uniqueness of some girth eight algebraically defined graphs, Part II,

*Discrete Applied Mathematics*, Volume 254, 15, (2019), pp. 161–170 [pdf] - The maximum number of colorings of graphs of given order and size: A Survey,

*Discrete Mathematics*, 342 (2019) pp. 2783–2791. [pdf] - (with S. DeWinter, R. Coulter and A. Kodess),

A Result on Polynomials Derived Via Graph Theory,

*Mathematics Magazine*Vol. 92 No. 4 (2019) pp. 288–295.[pdf] - (with L. Leshock),

On Pappus Configurations in Hall Planes,

to appear in*Designs, Codes and Cryptography*, 2022 [pdf] - (with V. Taranchuk),

A New Family of Algebraically Defined Graphs With Small Automorphism Group,

*The Electronic Journal of Combinatorics,*29(1)(2022), P1.43, [pdf]

**Published book:**

- (with O. Byer and D.L. Smeltzer),

Methods for Euclidean Geometry.

Mathematical Association of America, Inc., 2010, 1–461.

Published expository and teaching–oriented papers:

- Affine and Projective Planes,

*Y Sviti Matematiki,*6, 91-107, 1975 (In Ukrainian)

- Systems of Distinct Representatives,

*Y Sviti Matematiki,*7, 50–63, 1976 (In Ukrainian)

- On a Method in Algebra and Geometry,

*The AMATYC Reviews,*v. 12, No. 1 (1990), 70–72, and v. 12, No. 2 (1991) 47–48 [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, 261–266. [pdf] [ps]

- (with M.H. Klin, G. Poschel, V.I. Suschansky, V.A. Ustimenko, V.I. Vyshensky),

Lev Arkad’evich Kaluznin

*Applicandae**Matematicae,*52:(1998) 5–18 MR 99m: 01091. [pdf]

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, 14–15, 2006.

[pdf file from the journal] or [pdf file; preprint(shorter)]

- Surprises.
*The Mathematics Magazine, Vol.*87, No. 3, June 2014, 212–221. [pdf] - (with B. Kronenthal)

When can you factor a quadratic form?

*The Mathematics Magazine, Vol.*87, No. 1, February 2014, 25–36. - Herbert S. Wilf (1931–2012)

in the*Notices of the AMS*Volume 62, Number 4, April 2015, 346–360. [pdf] - Patricia Miller Overdeer: An Educator and Alumna.

*Reckonings,*Newsletter of the Department of Mathematical Sciences,

Summer 2014 and 2015, 22–23. [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]

**Research Reports:**

- (joint work with D.K. Garnick and Y.H.H. Kwong),

Graphs without Tree-Cycles or Four-Cycles for each order from 25 to 200

*Research. Rep.*91-2, 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 99-93, December 1993 - (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)