Mathematics Research 


Most of my publications are indexed in the ACM Digital Library, MathSciNet, SCI Expanded and zbMATH databases.

Prime labelings of trees. — in preparation.

The structure of the unit group in Z[Cx Crs], where r and s are distinct primes. — in preparation.

On the 4x4x2 tensors over the finite field F2. — in preparation.

A map of the P-positions in ‘Nim with a Pass’ played on heap sizes of at most four. — in revision.

Contributions to balanced arrays of strength ten and fractional factorial designs of resolution eleven. — submitted for publication.

On friendly index sets of n-galaxies. — submitted for publication.

The integer-magic spectra and null sets of the Cartesian product of two trees. — submitted for publication.

[60] Low, R.M. and Kapbasov, A., Non-attacking bishop and king positions on regular and cylindrical chessboardsJ. Integer Seq. 20 (2017), no. 6, Art. 17.6.1, 26 pp.

[59] Berlekamp, E. and Low, R.M., Entrepreneurial chess. — to appear in Internat. J. Game Theory. (2017). 

[58] Stavrou, S.G., Low, R.M. and Hernandez, N.J., Corrigendum to “Rank classification of 2x2x2x2x2 tensors over F2". — to appear in Linear and Multilinear Algebra. (2017).

[57] Vobbilisetty, R., Troia, F.D., Low, R.M., Corrado, V.A. and Stamp, M., Classic cryptanalysis using hidden Markov modelsCryptologia. 41 (2017), 1-28.

[56] Shiu, W.C. and Low, R.M., The integer-antimagic spectra of dumbbell graphs. Bull. Inst. Combin. Appl. 77 (2016), 89-110.

[55] Low, R.M. and Chan, W.H., Notes on the combinatorial game: Graph NimElectron. J. Graph Theory Appl. (2016), no. 2, 190-205.

[54] Stavrou, S.G., Low, R.M. and Hernandez, N.J., Rank classification of 2x2x2x2x2 tensors over F2Linear Multilinear Algebra. 64 (2016), no. 11, 2297-2312. 

[53] Bilgin, T., Kusmus, O. and Low, R.M., A characterization of the unit group in Z[T x C2]. Bull. Korean Math. Soc. 53 (2016), no. 4, 1105-1112.

[52] Roberts, D. and Low, R.M., Group-antimagic labelings of multi-cyclic graphsTheory and Applications of Graphs. Vol. 3: Iss. 1, Article 6 (2016). 

[51] Shiu, W.C. and Low, R.M., Integer-antimagic spectra of complete bipartite graphs and complete bipartite graphs with a deleted edge. Bull. Inst. Combin. Appl. 76 (2016), 54-68.

[50] Shiu, W.C., Sun, P.K. and Low, R.M., Integer-antimagic spectra of tadpole and lollipop graphs. Congr. Numer. 225 (2015), 5-22.

[49] Chopra, D.V., Low, R.M. and Dios, R., A note on resolution nine factorial designs using coincidences. Congr. Numer. 223 (2015), 219-226.

[48] Low, R.M. and Chan, W.H., An atlas of N- and P-positions in 'Nim with a Pass'Integers. 15 (2015), #G2, 14pp. (electronic).

[47] Chopra, D.V., Low, R.M. and Dios, R., A note on discrete factorial designs of resolution five and seven and balanced arrays. JCMCC. 90 (2014), 159-165.

[46] Oza, A., Ross, K., Low, R.M. and Stamp, M., HTTP attack detection using n-gram analysis. Computers and Security45 (2014), 242-254.

[45] Chang, K., Low, R.M. and Stamp, M., Cryptanalysis of TypexCryptologia. 38 (2014), 116-132.

[44] Chan, W.H., Low, R.M. and Shiu, W.C., Group-antimagic labelings of graphs. Congr. Numer. 217 (2013), 21-31.

[43] Chopra, D.V., Low, R.M. and Dios, R., Contributions to fractional factorial designs of resolutions six and eight for 2m series and bi-level balanced arrays. Congr. Numer. 215 (2013), 129-136.

[42] Chopra, D.V., Low, R.M. and Dios, R., Further results on some bi-level balanced arrays using coincidences. JCMCC. 86 (2013), 171-181.

[41] Baysa, D., Low, R.M. and Stamp, M., Structural entropy and metamorphic malware. Journal of Computer Virology and Hacking Techniques. Vol. 9, no. 4, (2013), 179-192.

[40] Craigen, R., Faucher, G., Low, R.M. and Wares, T., Circulant partial Hadamard matrices. Linear Algebra Appl. Vol. 439, no. 11, (2013), 3307-3317.

[39] Viswanathan, G., Low, R.M. and Stamp, M., Kullback-Leibler divergence for masquerade detection. Journal of Network and Information Security. Vol. 1, no. 1, (2013), 44-53. 

[38] Shanmugam, G., Low, R.M. and Stamp, M., Simple substitution distance and metamorphic detection. Journal of Computer Virology and Hacking Techniques. Vol. 9, no. 3, (2013), 159-170.

[37] Shiu, W.C. and Low, R.M., Group-magic labelings of graphs with deleted edges. Australas. J. Combin. 57 (2013), 3-19.

[36] Dhavare, A., Low, R.M. and Stamp, M., Efficient cryptanalysis of homophonic substitution ciphersCryptologia. 37 (2013), 250-281.

[35] Shiu, W.C. and Low, R.M., The integer-magic spectra of bicyclic graphs without pendant. Congr. Numer. 214 (2012), 65-73.

[34] Chopra, D.V., Low, R.M. and Dios, R., Investigations on balanced arrays of strength eight using coincidences and moment matrix. Congr. Numer. 213 (2012), 133-141.

[33] Chopra, D.V., Low, R.M. and Dios, R., Existence of balanced arrays and the positive semi-definiteness of the moment matrix. JCMCC. 82 (2012), 77-85.

[32] Chan, W.H., Low, R.M., Shiu, W.C., Steinberger, J. and Wan, K.Y., On a switch-setting problem arising from a variation of the 'Lights Out' game. JP J. Algebra Number Theory Appl. 24 (2012), no. 2, 173-184.

[31] Runwal, N., Low, R.M. and Stamp, M., Opcode graph similarity and metamorphic detection. Journal in Computer Virology(2012), 37-52.

[30] Chopra, D.V., Low, R.M. and Dios, R., Further contributions to balanced arrays of strength seven with applications. Congr. Numer. 210 (2011), 73-78.

[29] Chopra, D.V. and Low, R.M., Balanced arrays and fractional factorial designs. Bulletin of the ISI Proceedings of the 58th World Statistics Congress 2011, Dublin, ISBN: 978-90-73592-33-9. 

[28] Chopra, D.V., Low, R.M. and Dios, R., Investigations on strength eight balanced arrays using some classical inequalities. JCMCC. 78 (2011), 235-243.

[27] Chopra, D.V., Low, R.M. and Dios, R., New results on the existence of some balanced arrays using moment matrices. Congr. Numer. 205 (2010), 105-112.

[26] Dios, R., Ho, Y-S., Lee, S-M., Lo, S-P. and Low, R.M., Splitting extension of paths and cycles which are edge-graceful. Congr. Numer. 205 (2010), 17-31.

[25] Chopra, D.V., Low, R.M. and Dios, R., Further contributions to balanced arrays of strength four. JCMCC. 74 (2010), 103-110.

[24] Chopra, D.V., Low, R.M. and Dios, R., Contributions to strength six balanced arrays using Holder and Minkowski inequalities. JCMCC. 72 (2010), 93-100.

[23] Shiu, W.C. and Low, R.M., Zk-magic labelings of fans and wheels with magic-value zero. Australas. J. Combin. 45 (2009), 309-316.

[22] Chopra, D.V., Low, R.M. and Dios, R., Strength six orthogonal arrays and their non-existence. JCMCC70 (2009), 41-48.

[21] Chopra, D.V. and Low, R.M., Contributions to balanced arrays of strength t with applications. Frontiers of Applied and Computational Mathematics, 104-110, World Sci. Publ., Hackensack, NJ, 2008.

[20] Low, R.M. and Shiu, W.C., On the integer-magic spectra of graphs. Congr. Numer. 191 (2008), 193-203.

[19] Chopra, D.V., Low, R.M. and Dios, R., On the maximum number of constraints for some balanced arrays. Congr. Numer. 190 (2008), 5-11.

[18] Shiu, W.C., Ling, M.H. and Low, R.M., The edge-graceful spectra of connected bicyclic graphs without pendant. JCMCC. 66 (2008), 171-185.

[17] Low, R.M., On the units of the integral group ring Z[G x Cp]. J. Algebra Appl. 7 (2008), no. 3., 393-403.

[16] Shiu, W.C. and Low, R.M., Ring-magic labelings of graphs. Australas. J. Combin. 41 (2008), 147-158.

[15] Chopra, D.V., Low, R.M. and Dios, R., Contributions to orthogonal arrays of strength six. Congr. Numer. 186 (2007), 193-198.

[14] Kanungo, S. and Low, R.M., Further analysis on the "king and rook vs. king on a quarter-infinite board" problem. Integers. 7 (2007), #G9, 7pp. (electronic).

[13] Shiu, W.C. and Low, R.M., Integer-magic spectra of sun graphs. J. Comb. Optim. 14 (2007), 309-327.

[12] Low, R.M. and Sue, L., Some new results on the integer-magic spectra of tessellation graphs. Australas. J. Combin. 38 (2007), 255-266.

[11] Stamp, M. and Low, R.M., Applied Cryptanalysis: Breaking Ciphers in the Real World, Wiley-IEEE Press, May 2007, ISBN: 978-0-470-11486-5.

[10] Shiu, W.C., Ling, M.H. and Low, R.M., The entire edge-graceful spectra of cycles with one chord. Congr. Numer. 183 (2006), 213-219.

[09] Low, R.M. and Stamp, M., King and rook vs. king on a quarter-infinite board. Integers6 (2006), #G3, 8pp. (electronic).

[08] Shiu, W.C. and Low, R.M., Group magicness of complete n-partite graphs. JCMCC. 58 (2006), 129-134.

[07] Low, R.M. and Lee, S-M., On the integer-magic spectra of tessellation graphs. Australas. J. Combin. 34 (2006), 195-210.

[06] Low, R.M. and Lee, S-M., On the products of group-magic graphs. Australas. J. Combin. 34 (2006), 41-48.

[05] Low, R.M., Stamp, M., Craigen, R. and Faucher, G., Unpredictable binary strings. Congr. Numer. 177 (2005), 65-75.

[04] Lee, S-M., Ho, Y-S. and Low, R.M., On the integer-magic spectra of maximal planar and maximal outerplanar graphs. Congr. Numer. 168 (2004), 83-90.

[03] Low, R.M. and Lee, S-M., On group-magic Eulerian graphs. JCMCC. 50 (2004), 141-148.

[02] Low, R.M., Units in Integral Group Rings for Direct Products. Ph.D. Thesis, Dept. of Mathematics, Western Michigan University, (1998).

[01] Cabaniss, S., Low, R.M. and Mitchem, J., On edge-graceful regular graphs and trees. Ars Combin. 34 (1992), 129-142.