Ph. D. theses advised

• Dorota Kuziak, Resolvability and strong resolvability in product graphs. Rovira i Virgili University. In progress since 2010. Single advisor.

• Ismael González Yero, Contribution to the study of alliances in graphs. Rovira i Virgili University.  Date of public reading: December 13, 2010. Mark: "Sobresaliente cum laude". Single advisor.

• José María Sigarreta Almira, Alliances in Graphs. University Carlos III of Madrid. Date of public reading: June 1, 2007. Mark: "Sobresaliente cum laude". Single advisor.

---

Coauthors

José Luis Andrés Yebra (Spain), Sergio Bermudo (Spain), Josep Domingo-Ferrer (Spain), Ernesto Estrada (UK), Henning Fernau (Germany), Cristina García-Moreno (Spain), Ismael González Yero (Spain), Amauri Gutiérrez (Spain), Ivan Gutman (Servia), Aida Kamišalić (Slovenia), Dorota Kuziak (Poland), Magdalena Lemańska (Poland), Milan Randić (USA), José María Sigarreta (Mexico).

---

Refereed Journal Publications

 

1. Dorota Kuziak, Juan A. Rodríguez-Velázquez, Ismael G. Yero, Corrections to the article "The metric dimension of graph with pendant edges" [Journal of Combinatorial Mathematics and Combinatorial Computing, 65 (2008) 139--145]. Journal of Combinatorial Mathematics and Combinatorial Computing. To appear.
   
2. Henning Fernau, Juan A. Rodriguez-Velazquez and José M. Sigarreta. Global powerful r-alliances and total k-domination in graphs. Utilitas Mathematica. To appear.
3. Magdalena Lemańska, Juan A. Rodríguez-Velázquez and Ismael G. Yero. Nordhaus-Gaddum results for the convex domination number of a graph. Periodica Mathematica Hungarica.  To appear.
4. I. G. Yero and J. A. Rodriguez-Velázquez. On the Randic index of corona product graphs. ISRN-Discrete Matematics 2011 (2011) Article ID 262183, 7 pages. doi:10.5402/2011/262183.
   
5. Magdalena Lemańska, Juan A. Rodríguez-Velázquez and Ismael G. Yero. The limit case of a domination property. Acta Mathematica Sinica, English Series 28 (3) (2012)  463-468.
6. Ismael G. Yero and Juan A. Rodríguez-Velázquez, Partitioning a graph into global powerfull k-alliances. Graphs and Combinatorics. DOI: 10.1007/s00373-011-1065-7.   To appear.
7. Ismael G. Yero, Dorota Kuziak and Juan A. Rodríguez-Velázquez, On the metric dimension of corona product graphs. Computers and Mathematics with Applications 61 (9) (2011) 2793–2798. 
8. Ismael G. Yero,  Juan A. Rodríguez-Velázquez. Boundary powerful k-alliances in graphs.  Ars Combinatoria. To appear.
9. José M.  Sigarreta, Ismael G. Yero, Sergio Bermudo and Juan A. Rodríguez-Velázquez. Partitioning a graph into offensive k-alliances. Discrete Applied Mathematics 159 (4) (2011) 224–231.
10. I. G. Yero, S. Bermudo, J. A. Rodríguez-Velázquez and J. M. Sigarreta. Partitioning a graph into defensive k-alliances.  Acta Mathematica Sinica, English Series 27 (1) (2011) 73–82. 
11. Juan A. Rodríguez-Velázquez, José M. Sigarreta, Ismael G. Yero and Sergio Bermudo. Alliance free and alliance cover sets.  Acta Mathematica Sinica, English Series 27 (3)  (2011)  497-504.
12. Ismael G. Yero and Juan A. Rodríguez-Velázquez. A note on the partition dimension of Cartesian product graphs. Applied Mathematics and Computation 217 (7) (2010) 3571–3574.
13. Sergio Bermudo, Juan A. Rodríguez-Velázquez, Ismael G. Yero and José M. Sigarreta. On global offensive k-alliances in graphs. Applied Mathematics Letters  23 (12) (2010) 1454–1458. 
14. Ismael  G. Yero, Juan A. Rodríguez-Velázquez and Ivan Gutman. Estimating the higher-order Randić index.  Chemical Physics Letters 489 (1–3) (2010) 118–120.  
15. Ismael G. Yero,  Juan A. Rodríguez-Velázquez. Boundary defensive k-alliances in graphs.  Discrete Applied Mathematics 158 (11) (2010) 1205–1211.
16. S. Bermudo, J. A. Rodríguez-Velázquez, J. M. Sigarreta and I. G. Yero.  On geodetic and k-geodetic sets in graphs. Ars Combinatoria 96 (2010) 469–478.
17. Juan Alberto Rodríguez-Velázquez, Aida Kamisalic and Josep Domingo-Ferrer. On reliability indices of communication networks.  Computers and Mathematics with Applications 58 (7) (2009) 1433–1440.
18. J. A. Rodríguez.  Laplacian eigenvalues and partition problems in hypergraphs.  Applied Mathematics Letters 22 (6) (2009) 916–921.
19. Henning Fernau, Juan A. Rodríguez and José M. Sigarreta. Offensive r-alliances in graphs.  Discrete Applied Mathematics 157 (1) (2009) 177–182.
20. Juan A. Rodríguez-Velázquez, Ismael G.Yero and José M. Sigarreta. Defensive k-alliances in graphs.  Applied Mathematics Letters 22 (1) (2009) 96–100.
21. J. A. Rodríguez-Velázquez and J. M. Sigarreta. Global defensive k-alliances in graphs.  Discrete Applied Mathematics 157 (2) (2009) 211–218.
22. J. M. Sigarreta and J. A. Rodríguez. On the global offensive alliance number of a graph. Discrete Applied Mathematics 157 (2) (2009) 219–226.
23. J. A. Rodríguez, E. Estrada and A. Gutiérrez. Functional centrality in graphs.  Linear and Multilinear Algebra 55 (3) (2007) 293–302.
24. Juan Alberto Rodríguez -Velázquez and José  María Sigarreta Almira. Spectral study of alliances in graphs  Discussiones Mathematicae Graph Theory 27 (1) (2007) 143–157.
25. I. Gutman, E. Estrada and J. A. Rodríguez-Velázquez. On a graph-spectrum-based structure descriptor.  Croatica Chemica Acta 80 (2) (2007) 151–154.
26. J. A. Rodríguez-Velázquez and J. M. Sigarreta. Global alliances in planar graphs.  AKCE–International Journal of Graphs and Combinatorics 4 (1) (2007) 83–98.
27. J. A. Rodríguez and J. M. Sigarreta. Offensive alliances in cubic graphs.  International Mathematical Forum 1 (36) (2006) 1773–1782.
28. J. A. Rodríguez.  The (α, β,s,t)-diameter of graphs: A particular case of conditional diameter.  Discrete Applied Mathematics 154 (14) (2006) 2024–2031.
29. J. A. Rodríguez-Velázquez and J. M. Sigarreta. Global offensive alliances in graphs.  Electronic Notes in Discrete Mathematics 25 (2006) 157–164.
30. J. M. Sigarreta and J. A. Rodríguez. On defensive alliances and line graphs.  Applied Mathematics Letters 19 (12) (2006) 1345–1350.
31. Ernesto Estrada and Juan A. Rodríguez-Velázquez. Subgraph centrality and clustering in complex hyper-networks.  Physica A 364 (2006) 581–594.
32. Ernesto Estrada, Juan A. Rodríguez-Velázquez and Milan Randić. Atomic branching in molecules.  International Journal of Quantum Chemistry 106 (4) (2006) 823–832.
33. J. A Rodríguez and J. M. Sigarreta.  On the Randić index and conditional parameters of a graph.  MATCH Commun. Math. Comput. Chem. 54 (2) (2005) 403–416.
34. J. A. Rodríguez. A spectral approach to the Randić index.  Linear Algebra and its Applications 400 (2005) 339–344.
35. J. A. Rodríguez. On the Wiener index and the eccentric distance sum of hypergraphs.  MATCH Commun. Math. Comput. Chem. 54 (1) (2005) 209–220.
36. Ernesto Estrada and Juan A. Rodríguez-Velázquez. Subgraph centrality in complex networks.  Physical Review E 71 (5) 056103 (2005) 9 pages.
37. Ernesto Estrada and Juan A. Rodríguez-Velázquez. Spectral measures of bipartivity.  Physical Review E 72 (4) 046105 (2005) 6 pages.
38. J. A. Rodríguez. On the Laplacian spectrum and walk-regular hypergraphs.  Linear and Multilinear Algebra 51 (3) (2003) 285–297.
39. J. A. Rodríguez. On the Laplacian eigenvalues and metric parameters of hypergraphs.  Linear and Multilinear Algebra 50 (1) (2002) 1–14.
40. J. A. Rodríguez, A. Gutiérrez and J. L. A. Yebra. On spectral bounds for cutsets. Discrete Mathematics 257 (1) (2002) 101–109. 
41. J. A. Rodríguez and J.L.A. Yebra. Laplacian eigenvalues and the excess of a graph.  Ars Combinatoria 64 (2002) 249–258.  
42. J. A. Rodríguez and J.L.A Yebra. Bounding the diameter and the mean distance of a graph from its eigenvalues: Laplacian versus adjacency matrix methods.  Discrete Mathematics 196 (1–3) (1999) 267–275.

---

Submitted papers

• Ismael G. Yero, Juan A. Rodríguez-Velázquez and Sergio Bermudo. Alliance free sets in Cartesian product graphs.  Submitted
  

• Juan A. Rodríguez-Velázquez, Ismael G. Yero and Magdalena Lemańska. On the partition dimension of trees. Submitted.

• Juan A. Rodríguez-Velázquez, Ismael G. Yero and Dorota Kuziak,  Partition dimension of corona product graphs. Submitted.

• Ismael G. Yero and Juan A. Rodríguez-Velázquez. Analogies between the geodetic number and the Steiner number of some classes of graphs. Submitted.
  

• Juan Alberto Rodríguez-Velázquez, Ismael G. Yero and Henning Fernau, On the  partition dimension of  unicyclic graphs. Submitted.

• Ismael G. Yero and Juan A. Rodríguez-Velázquez, Roman domination in Cartesian product graphs and strong product graphs. Submitted.

• Dorota Kuziak, Ismael G. Yero and Juan A. Rodríguez-Velázquez, On the strong metric dimension of corona product graphs and join graphs. Submitted.

• Ismael G. Yero and Juan A. Rodríguez-Velázquez, Computing global offensive alliances in Cartesian product graphs. Submitted.

• M. Lemanska, J. A. Rodriguez-Velazquez and R. Trujillo-Rasua, Analogies and discrepancies between the vertex cover number and the weakly connected domination number. Submitted.
  

---

Refereed Conference Publications

• Juan A. Rodríguez-Velázquez, Ismael G. Yero, Some bounds on the partition dimension of trees and unicyclic graphs. "VII Encuentro Andaluz de Matemática Discreta" (2011). Abstracts 125-132. ISBN: 978-84-694-5627-9
• Juan A. Rodríguez-Velázquez, Ismael G. Yero and Dorota Kuziak. Partition dimension of corona product graphs. 7th. Slovenian International Conference on Graph Theory, Bled'11, Bled, Slovenia, 19-25 June 2011. Abstracts 123-124.

 

• Ismael G. Yero, Juan A. Rodriguez-Velazquez and Magdalena Lemanska. On the partition dimension of Cartesian product graphs. Cologne-Twente Workshop on Graphs and Combinatorial Optimization CTW10, University of Cologne, Germany. May 25-27, 2010. Abstracts 61-64.

 

• Sergio Bermudo, Juan A. Rodríguez-Velázquez, José M. Sigarreta and Ismael G. Yero. On geodetic sets of a graph. Colourings, Independence and Domination: 13th Workshop on Graph Theory, CID-2009.  September 20-25, 2009, Szklarska Poreba, Poland. Abstracts 86-87.

 

• José M. Sigarreta, Ismael G. Yero, Sergio Bermudo and Juan A. Rodríguez-Velázquez. Partitioning a graph into offensive k-alliances. Cologne-Twente Workshop on Graphs and Combinatorial Optimization CTW09, Paris, France. June 2-4, 2009. Abstracts 297-300.

 

• J. A. Rodríguez-Velázquez and Aida Kamišalić. The Laplacian spectrum of hypergraphs. 15-th Conference of the International Linear Algebra Society, ILAS-2008 Cancún, México. Abstracts 60-61

 

• H. Fernau, J. A. Rodríguez-Velázquez and J. M. Sigarreta. Global r-alliances and total domination. Cologne-Twente Workshop on Graphs and Combinatorial Optimization 2008. Università degli Studi di Milano, Gargnano, Italy. Abstracts 98-101

 

• Juan A. Rodríguez-Velázquez and José M. Sigarreta. On the defensive k-alliance number of a graph. Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW-2007. University of Twente, Enschede, The Netherlands. Abstracts 133-136, ISBN: 1574-0846

 

• Juan Alberto Rodríguez Velázquez, Ismael González-Yero and José María Sigarreta. Mathematical properties of k-Web Communities INFORMATICA - 2007. III Taller Internacional de Calidad en las Tecnologías de la Informa ción y las Comunicaciones. La Habana, Cuba (2007) Proceedings ISBN: 978-959-286-002-5. CAL-019, 9 pages.

 

• Juan A. Rodríguez-Velázquez and Cristina García-Moreno. Functional centrality: A centrality measure for social networks analysis. COMPUMAT-2007. Holguín, Cuba. Boletín de la Sociedad Cubana de Matemática y Computación 5 (Número especial) MDC9 (2007) 6 pages. ISSN 1728-6042

 

• J. A. Rodríguez-Velázquez, J. M. Sigarreta and I. G. Yero. Global defensive k-alliances in graphs. COMPUMAT-2007. Holguín, Cuba. Boletín de la Sociedad Cubana de Matemática y Computación 5 (Número especial) MDC8 (2007) 6 pages. ISSN 1728-6042

 

• J. A. Rodríguez and J. M. Sigarreta. Defensive alliances in graphs. International Congress of Mathematicians. Madrid 2006, Abstracts 489-490.

 

• J. M. Sigarreta and J. A. Rodríguez. Global offensive alliances in graphs. Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW-2006. Lambrecht, Germany. Abstracts 122-130.

 

• J. A. Rodríguez and J. M. Sigarreta. On the degree-adjacency matrix of a graph. 17th International Conference on Formal Power Series and Algebraic Combinatorics. FP SAC 05. Messina, Italy (2005) Paper N. 41, 14 pages.

 

• J. A. Rodríguez y J.L.A Yebra. Cotas espectrales del exceso y la excentricidad de un conjunto de vértices de un grafo. EAMA-97 Sevilla, Spain (1997) Abstracts 383-390. ISBN: 84-605-6586-6.

 

• J. A. Rodríguez and J.L.A Yebra. Bounds of the excess of a graph based on the eigenvalues of its Laplacian matrix. IVth Symposium of Mathematics. Inst. Cibern. Mat. Fis., Havana (1997) Abstracts 80-91. ISBN: 959-02-0239-X. 

 

• Ángel A. Juan, María A. Huertas, Cristina Steegmann, Juan A. Rodríguez, Manuel Terradez. Uso e integración de las TIC en asignaturas cuantitativas aplicadas. La experiencia de los estudios de informática y multimadia de la UOC.  XI congreso Universitario de Innovación Educativa en las Enseñanzas Técnicas (2003) R0184, ISBN 84-688-2216-7.

---

Other Publications

• Juan Alberto Rodríguez Velázquez. Cotas de diversos parámetros de un grafo a partir de los autovalores de su matriz laplaciana.   Ediciones UPC (1997) ISBN 84-7653-664-X

 

• Juan A. Rodríguez-Velázquez, Ismael G. Yero, Some bounds on the partition dimension of trees and unicyclic graphs. In "Avances en Matemática Discreta en Andalucía", Volume II. Edited by José Cáceres, Clara Grima, Alberto Márquez and María Luz Puertas. (2011) 125-132. ISBN: 978-84-694-5627-9

---

Editorial work

• Member of the “Editorial Board of American Journal of Computational and Applied Mathematics"  (from June 2011)

• Member of the Editorial Board of ISRN Discrete Mathematics.  ISSN (Print): 2090-777X,  ISSN(Online): 2090-7788  (from June of 2011)

• Member of the “Editorial Board of the Oriental Journal of Mathematics" ISSN Print 0975-7740, ISSN Online  0975-7759 (from July  of 2009)

Referee for scientific journals