College of Sciences & Technology

• Ph.D. Mathematics (Graph Theory/Combinatorics) from the University of Houston, Houston, Texas in 1997.
  
• M.A. in MS in Mathematics (Graph Theory/Combinatorics) from University of Houston, Houston, Texas in 1993.
  
• B.S. in Mathematics, Minor in CS, and a Teaching Certificate, from University of Texas/Pan American, Edinburg, Texas in 1989.​​
  

​​MATH 2405: Discrete Mathematics​​

• Associate Dean CST, University of Houston-Downtown, Houston, Texas, 2012 through present.
  
• Assistant Chair for Freshman Program CMS, University of Houston-Downtown, Houston, Texas, 2010 through 2012.
  
• Professor of Mathematics, Department of Mathematics and Statistics, University of Houston-Downtown, Houston, Texas, 2013 through present.
  
• Professor of Mathematics, Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Texas, 2010 through 2013.
  
• Associate Professor, Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Texas, 2003 through 2010.
  
• Assistant Professor, Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Texas, 1997 through 2003.
  
• Teaching Fellow/Lecturer, 
  
• Department of Mathematics, University of Houston, Houston, Texas, 1992 through 1997.
  
• Research Assistant, Department of Mathematics, UH, Houston, Texas, Research supported in part by grant 003652085-ARP, 1990 through 1992.
  

Publications

1. E. DeLaViña and C. E. Larson, A parallel algorithm for computing the critical independence number and related sets, ARS Mathematica Contemporanea (2013), Vol. 6(2), (PDF reprint)
2. E. DeLaViña,  C. E. Larson, R. Pepper and B. Waller and, A characterization of graphs where the independence number equals the radius, Graphs and Combinatorics (2012), Vol. 28, 315-332. (PDF reprint)
3. E. DeLaViña and R. Pepper, Graffiti.pc on the k-independence number of a graph, Proceedings of the Forty Third Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, (2012), Vol. 213, 185-195. (PDF reprint)
4. E. DeLaViña, R. Pepper and B. Waller, Graffiti.pc on the independent-domination number of a graph, Proceedings of the Fortieth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, (2011), Vol. 209, 17-25. (PDF preprint).
5. E. DeLaViña, W. Goddard, M. A. Henning, R. Pepper, and E. Vaughn,  Bounds on the k-domination number of a graph, Applied Mathematics Letters (2011), Vol. 24 (6), 996-998 (PDF preprint).
6. E. DeLaViña, C. Larson, R. Pepper and B. Waller, Graffiti.pc on the 2-domination number of a graph, Proceedings of the Forty-first Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, (2010), Vol. 203, 15-32 (pdf preprint).
7. E. DeLaViña, R. Pepper and B. Waller, Lower bounds for the domination number (pdf preprint), Discussions Mathematicae Graph Theory, (2010), Vol. 30(3), 475-487.
8. E. DeLaViña, C. Larson, R. Pepper and B. Waller, On total domination and support vertices of a tree ( pdf preprint), AKCE J. Graphs. Combin., (2010), Vol. 7 (1), 85-95.
9. E. DeLaViña, C. Larson, R. Pepper and B. Waller, Graffiti.pc on the total domination number of a tree, Proceedings of the Fortieth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, (2009), Vol. 195, 5-18. (pdf preprint)
10. S. Yuan, W. Waller, E. DeLaViña, Heuristic algorithms for finding reliable lightpath under multiple failures, Ultra Modern Telecommunications and Workshops, Oct. (2009), ICUMT '09, pp.1-7.
11. E. DeLaViña, R. Pepper and B. Waller, A note on dominating sets and average distance, Discrete Mathematics (2009), Vol. 309 (8), 2615-2619. (pdf preprint)
12. E. DeLaViña and I. Gramajo, Some elementary bounds on the matching number of bipartite graphs, Bulletin of the ICA (2008), Vol. 54, 93-102. (pdf preprint)
13. E. DeLaViña and B. Waller, Spanning trees with many leaves and the average distance, Electronic Journal of Combinatorics (2008), Vol. 15 (1).
14. E. DeLaViña, Q. Liu, R. Pepper, B. Waller and D. B. West, On some conjectures of Graffiti.pc on total domination, Proceedings of the Thirty-Seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, (2007), Vol. 185, 81-95. (pdf preprint)
15. E. DeLaViña, R. Pepper and B. Waller, Independence, radius and Hamiltonian paths, MATCH Commun. Math. Comput. Chem: proceedings of the conference "Computers in Scientific Discovery III", Ghent, February 6-9, 2006 (eds. G. Brinkmann, P. W. Fowler) (2007) Vol. 58, pp. 481-510. (pdf preprint)
16. E. DeLaViña, Some history of the development of Graffiti, Graphs and Discovery DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, (2005) Vol. 69, 81-118. (pdf preprint)
17. E. DeLaViña, S. Fajtlowicz and B. Waller, On conjectures of Griggs and Graffiti (pdf), Graphs and Discovery DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, (2005), Vol. 69, 119-125.(pdf preprint)
18. E. DeLaViña, Graffiti.pc: a variant of Graffiti, Graphs and Discovery DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, (2005), Vol. 69, 71-79. (pdf preprint)
19. E. DeLaViña and B. Waller, On some conjectures of Graffiti.pc on the maximum order of induced subgraphs, Proceedings of the Thirty-Fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium, (2004), Vol. 166, 11-32. (pdf preprint)
20. E. DeLaViña and B. Waller, Independence, radius and path coverings in trees, Proceedings of the Thirty-third Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2002).Congressus Numerantium, (2002), Vol. 156, 155-169. (pdf preprint)
21. E. DeLaViña, Graffiti.pc, Graph Theory Notes of New York, (2002), XLII, 26-30. (pdf preprint)
22. E. DeLaViña, Ramseyan Properties of Connected Triangle-Free Graphs, Proceedings of the Thirty-second Southeastern International Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 2001). Congressus Numerantium (2001), Vol. 148, 185-192.
23. E. DeLaViña, On Graffiti’s 781 About Jets of Independent Sets and the Szekeres-Wilf Invariant, Bulletin of the ICA (1998), Vol. 24, 47-50.
24. C. Campbell, E. DeLaViña and F. Harary, Maximum Induced Circumference, Pan American Journal of Mathematics (1997), Vol. 7, No. 2, 37-39.
25. E. DeLaViña and S. Fajtlowicz, Ramseyan properties of graphs, Electronic Journal of Combinatorics (1996), Vol. 3.

Other Publications

1. E. DeLaViña and D. Schaal, Working with local students, Proceedings of the conference on promoting undergraduate research in mathematics, American Mathematical Society (2007), pp.377-380.

To Appear

1. E. DeLaViña, C. Larson, R. Pepper and B. Waller, Graffiti.pc on the 2-domination number of a graph (pdf preprint), 2010.

Preprints

1. E. DeLaViña and C. E. Larson, A parallel algorithm for computing the critical independence number and related sets, 2010.
2. E. DeLaViña, W. Goddard, M. A. Henning, R. Pepper, and E. Vaughn,  Bounds on the 2-domination number of a graph, 2010.
3. E. DeLaViña and B. Waller, A note on a conjecture of Hansen et. al., (pdf preprint), 2009.
4. E. DeLaViña,  C. E. Larson, R. Pepper and B. Waller and, A characterization of graphs where the independence number equals the radius, 2008.

In Preparation 

1. D. Amos and E. DeLaViña, New bounds on the total domination number of a graph, 2012.
2. E. DeLaViña and C. E. Larson, on the union of critical independent sets, 2010.

Field of Specialization

Graph Theory, with an emphasis on graph theoretical induced substructures, variations of Ramsey theory, extremal graph theory, and invariants related to independent sets in graphs.