College of Natural Sciences, Room C-119

Department of Mathematics

P.O.Box 70377, San Juan, PR 00936-8377

Phone number: (787) 764-0000, ext. +1 4711

Fax number: (787) 281-0651

- (with O. Tomaiconza)
**Nonexistence of Efficient Dominating Sets in the Cayley Graphs of Transposition Trees of Diameter 3**, draft available here, or in a shorter version, see Selected Publications. **Rainbow Coloring of Bipartite Graphs**, available here.**Structure of Odd-Girth Cycles in Odd Graphs**, available here.**Ordering the Levels L**, available here._{k}and L_{k+1}of B_{2k+1}**Connected Edge-Disjoint Unions of Turan Graphs**, available here.-
**Asymptotic Diameter of Graphs**, available here. - (with K. T. Phelps)
**On Perfect Domination of Binary Cubes**, available here.

- (with O. Tomaiconza)
**Nonexistence of Efficient Dominating Sets in the Cayley Graphs of Transposition Trees of Diameter 3**to appear in Discrete Applied Mathematics, available here. **On a K**, to appear in JCMCC, volume 95, November 2015, 127-146, available here._{4}-UH Self-Dual 1-Configuration (102_{4})_{1}**Rainbow Tetrahedra in Cayley graphs**, Discussiones Mathematicae Graph Theory, 35 (2015) 733-754 doi:10.7151/dmgt, available here.**Pappus-Desargues Digraph Confrontation****, JCMCC, May 2014, volume 89, 101-111 available here.****Worst-Case Efficient Dominating Sets in Digraphs**, Discrete Applied Mathematics, 161 (2013) 944-952; doi 10.1016/j.dam.2012.11.016, available here.- (with C. Araujo)
**Lattice-Like Total Perfect Codes**, Discussiones Mathematicae Graph Theory, volume 34(2014), 57-74, doi:10.7151/dmgt.1715, available here. - (with C. Araujo and P. Horak)
**A Generalization of Lee Codes**, Designs, Codes and Cryptography, Online First, 2012, DOI: 10.1007/s10623-012-9666-6; January 2014, Volume 70, Issue 1-2, pp 77-90, available here. **Orienting and Separating Distance-Transitive Graphs**, Ars Mathematica Contemporanea, 5, (2012), 221-236, available here.**From the Coxeter Graph to the Klein Graph**, Journal of Graph Theory, 70 (2012), 1-9, available here.- (with E. J. Billington, D. Hoffman and C. C. Lindner)
**Almost Resolvable Maximum Packings of Complete Graphs with 4-cycles**, Graphs and Combinatorics 27, (2011), 161-170, available here. **Star Graphs: Threaded Distance Trees and E-sets**, JCMCC, 77, (2011), 3-16, available here,**On a C**, Discrete Mathematics, 310, (2010), 1389-1391, available here._{4}-Ultrahomogeneous Oriented Graph**On a {K**, Australasian Journal of Combinatorics, 44, (2009), 63-75, available here, by courtesy of http://ajc.maths.uq.edu.au and with two posterior corrigenda in Section 3: item (2) of line 3 (reported) and lines 26-27, where it should say 347,356,246,257;257,356,246,347;257,347,247,456._{4},K_{2,2,2}}-Ultrahomogeneous Graph- (with A. A. Delgado)
**Perfect Domination in Rectangular Grid Graphs**, JCMCC, 70, (2009), 177--196. available here. A larger version of this manuscript is available here **Quasiperfect Domination in Triangular Lattices**, Discussiones Mathematicae Graph Theory, 29(1), (2009), 179-198, available here.**Perfect Domination in Regular Grid Graphs**, Australasian Journal of Combinatorics, 42, (2008), 99-114, available here, by courtesy of http://ajc.maths.uq.edu.au.**SQS-graphs of extended 1-Perfect Codes**, Congressus Numerantium, 193, (2008), 175-194, available here. A newer version of this publication,**SQS-Graphs of Solov'eva-Phelps Codes**, can be found here.- (with C. C. Lindner, C. A. Rodger and M. Meszka)
**Almost Resolvable 4-Cycle Systems**, JCMCC, 63, (2007), 173 - 182, available here; with a Corrigendum/Addendum in JCMCC, 66, (2008), 297-298, available here, containing a kind contribution by E. J. Billington, consisting in using the corrected Example 2.1, contributed by Dejter, that provided an almost resolvable 4-cycle system of order n = 17, to construct one of the missing cases, namely the one whose order is n = 33. (Cases n = 41 and 57 are still not known). - (with A. A. Delgado)
**Classes of Hamilton Cycles in the 5-Cube**, JCMCC, 61, (2007), 81-95, available here. (NOTE: Reference [3] at the end of this paper can be found in http://home.coqui.net/dejterij/mcns/mirame.txt), as the original site http://www.cnnet.edu became defunct. - (with A. A. Delgado)
**STS-Graphs of Perfect Codes mod Kernel**, Discrete Mathematics 295, (2005), 31-47, available here. - (with O. Serra)
**Efficient Dominating Sets in Cayley graphs**, Discrete Applied Mathematics 129, (2003), 319-328, available here. -
**Equitable Factorizations of Hamming Shells**, Discrete Mathematics 261, (2003), 177-187, available here. - (with K. T. Phelps)
**Ternary Hamming and Binary Perfect Covering Codes**, in: A. Barg and S. Litsyn, eds., Codes and Association Schemes, DIMACS Ser. Disc. Math. Theor. Comp. Sci, 56, (2001), 111-113, available here. -
**Excluded Minors for [2,3]-Graph Planarity**, JCMCC, 35, (2000), 117-125, available here. - (with D. A. Pike and C. A. Rodger)
**The Directed Almost Resolvable Hamilton-Waterloo Problem**, Australasian J. Combinat., 18, (1998), 201-208, available here. - (with H. Hevia and O. Serra)
**Hidden Cayley Graph Structures**, Discrete Math., 182, (1998), 69-83, available here. - (with F. Franek, E. Mendelsohn and A. Rosa)
**Triangles in 2-Factorizations**, J. Graph Theory, 26, (1997), 83-94, available here. -
**Symmetry of factors of the 7-Cube Hamming Shell**, J. Combinatorial Designs, 5, (1997), 301-309, available here. - (with F. Franek and A. Rosa)
**A Completion Conjecture for Kirkman Triple Systems**, Utilitas Math., 50, (1996), 97-102, available here. -
**TMC Tetrahedral Types MOD 2k+1 and their Structure Graphs**, Graphs and Combinatorics, 12, (1996), 163-178, available here. - (with J. Borges)
**On Perfect Dominating Sets in Hypercubes and their Complements**, JCMCC, 20, (1996), 161-173, available here. - (with R. Giudici)
**On Unitary Cayley graphs**, JCMCC 18, (1995), 121-124. available here. -
**Network Models Encoded by Weighted Tetrahedra**, in Y. Alavi et al. eds., Proc. 7th Int. Conf. Theory & Appl. Graphs, vol 1, 1995, 289-300, available here. - (with J. Pujol)
**Perfect Domination and Symmetry in Hypercubes**, Congr. Num., 111, (1995), 18-32, available here. -
**On Symmetric Subgraphs of the 7-Cube: an overview**, Discrete Math., 124, (1994), 55-66, available here. - (with A. Rosa and P. I. Rivera-Vega)
**Invariants for 2-Factorizations and Cycle Systems**, JCMCC, 16, (1994), 129-152, available here. **Recognizing the Hidden Structure of Cayley Graphs**, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 15, (1994), 379-389, available here.- (with W. Cedeno and V. Jauregui)
**A Note on Frucht diagrams, Boolean graphs and Hamilton cycles**, Discrete Mathematics, 114, (1993), 131-135, available here. - (with P. Weichsel)
**Twisted Perfect Dominating Subgraphs of Hypercubes**, Congr. Num., 94, (1993), 67-78, available here. - (with A. E. Brouwer and C. Thomassen)
**Highly Symmetric Subgraphs of Hypercubes**, Jour. Alg. Combin., 2, (1993), 25-29, available here. -
**(with V. Neumann-Lara)****Voltage Graphs and Hamilton Cycles**, Advances in Graph Theory, V. R. Kulli ed., Vishwa Int. Publ., (1991), 141-153, available here. - (with P. Guan)
**Square-Blocking Edge Subsets in Hypercubes and Vertex Avoidance**, Y. Alavi et al. (eds.), Combin., Algor, & Appls., SIAM Proc., Philadelphia (1991), 162-174, available here. -
**Quarter-Turns and Hamiltonian Cycles for Annular Chessknight Graphs**, Scientia Ser A, Math Sci, 4, (1990/1991), 21-29, available here. -
**(1,2k)-Chessknight Hamilton cycles Invariant under Quarter Turns**, Scientia Ser A, Math Sci, 2, (1988), 39-51, available here. **Totally Multicolered Subgraphs of Complete Cayley Graphs**, Congressus Num., 70, (1990), 53-64, available here.**Minimal Hamiltonian and Nonhamiltonian Covering graphs of K**, Ars Combinatoria, 25-C, (1988), 63-71, available here._{n}- (with J. Cordova and J. Quintana)
**Two Hamilton Cycles in Bipartite Reflective Kneser Graphs**, Discrete Mathematics, 72, (1988), 63-70, available here. - (with V. Neumann-Lara)
**Unboundedness for Generalized Odd Cyclic Transversality**, Colloquia Mathematica Societatis J\'anos Bolyai, 52, Combinatorics, Eger (Hungary), (1987), 195-203, available here. **Vertex specular covering graphs and their properties**, Colloquia Mathematica Societatis J\'anos Bolyai, 52, Combinatorics, Eger (Hungary), (1987), 545-546, available here.- (with J. Quintana)
**On an Extension of a Conjecture of I. Havel**, in Graph Theory, Combin., and Appls., eds. Y. Alavi et al., (1991), J. Wyley and sons, 327-341, available here. - (with J. Quintana)
**Long Cycles in Revolving Door Graphs**, Congressus Num., 60, (1987), 163-168, available here. **Unfolding m-Genus Tori around Cayley Graphs**, Ars Combinatoria, 25-C, (1985), 125-133, available here.-
**Hamilton Cycles and Quotients of Bipartite Graphs**, in Y. Alavi et al. (eds), Graph Theory & Appls. Algor. & Comp. Sci., Wyley (1985), 189-199, available here. **Equivalent Conditions for Euler's Problem on $Z_4$-Hamiltonian cycles**, Ars Combinatoria, 16-B, (1983), 285-295, available here.

**Video of the presentation "A Generalization of Lee Codes" (joint with Carlos Araujo and Peter Horak) on Monday, September 12, 10.00am-10.20am.****Accompanying slides.****Some pictures of the 3ICMCTA.**