Juan Alberto Rodr´ıguezVel´azquez,Ph. D. Departament d’Enginyeria Inform`aticai Matem`atiques Universitat Rovira i Virgili Av. Pa¨ısos Catalans, 26 43007 Tarragona E-mail: [email protected]

Research interests

My primary research interest is graph theory.

Ph. D. theses advised

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

Ismael Gonz´alezYero, 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.

Jos´eMar´ıaSigarreta Almira, Alliances in Graphs. University Carlos III of Madrid, Docto- ral Programme in Mathematical Engineering. Date of public reading: June 1, 2007. Mark: Sobresaliente cum laude. Single advisor.

Coauthors

Jos´eLuis Andr´esYebra (Spain), Sergio Bermudo (Spain), Josep Domingo-Ferrer (Spain), Ernesto Estrada (UK), Henning Fernau (Germany), Cristina Garc´ıa-Moreno (Spain), Ismael Gonz´alezYero (Spain), Amauri Guti´errez(Spain), Ivan Gutman (Servia), Aida Kamiˇsali´c(Slove- nia), Dorota Kuziak (Poland), Magdalena Lema´nska (Poland), Milan Randi´c(USA), Jos´eMar´ıa Sigarreta (Mexico). h-index, Jul. 2011

Scopus h-index: 9 Web of science h-index: 7 Google Scholar h-index: 12

Most cited article

• Subgraph in complex networks Ernesto Estrada and Juan A. Rodr´ıguez-Vel´azquez Physical Review E 71 (5) 056103 (2005) 9 pages. Citations 108 (from Scopus), 42 (from the web of science), 189 (from Google Scholar)

Refereed Journal Publications

1. Nordhaus-Gaddum results for the convex domination number of a graph Magdalena Lema´nska, Juan A. Rodr´ıguez-Vel´azquezand Ismael G. Yero Periodica Mathematica Hungarica. In press.

2. The limit case of a domination property. Magdalena Lema´nska, Juan A. Rodr´ıguez-Vel´azquezand Ismael G. Yero Acta Mathematica Sinica, English Series 27 (8) (2011) In press.

3. Partitioning a graph into global powerfull k-alliances Ismael G. Yero and Juan A. Rodr´ıguez-Vel´azquez Graphs and Combinatorics. DOI: 10.1007/s00373-011-1065-7

4. On the metric dimension of corona product graphs. Ismael G. Yero, Dorota Kuziak and Juan A. Rodr´ıguez-Vel´azquez Computers and Mathematics with Applications 61 (9) (2011) 2793–2798.

5. Partitioning a graph into offensive k-alliances Jos´eM. Sigarreta, Ismael G. Yero, Sergio Bermudo and Juan A. Rodr´ıguez-Vel´azquez Discrete Applied Mathematics 159 (4) (2011) 224–231.

6. Alliance free and alliance cover sets Juan A. Rodr´ıguez-Vel´azquez,Jos´eM. Sigarreta, Ismael G. Yero and Sergio Bermudo Acta Mathematica Sinica, English Series 27 (3) (2011) 497–504.

7. Partitioning a graph into defensive k-alliances Ismael G. Yero, Sergio Bermudo, Juan A. Rodr´ıguez-Vel´azquez, and Jos´eM. Sigarreta Acta Mathematica Sinica, English Series. 27 (1) (2011) 73–82. 8. Boundary powerful k-alliances in graphs I. G. Yero and J. A. Rodr´ıguez-Vel´azquez Ars Combinatoria. In press.

9. Estimating the higher-order Randi´cindex Ismael G. Yero, Juan A. Rodr´ıguez-Vel´azquezand Ivan Gutman Chemical Physics Letters 489 (1–3) (2010) 118–120.

10. Boundary Defensive k-alliances in graphs. I. G. Yero and J. A. Rodr´ıguez-Vel´azquez Discrete Applied Mathematics 158 (2010) 1205–1211.

11. On geodetic and k-geodetic sets in graphs. S. Bermudo, J. A. Rodr´ıguez-Vel´azquez,J. M. Sigarreta and I. G. Yero. Ars Combinatoria 96 (2010) 469–478.

12. A note on the partition dimension of Cartesian product graphs. Ismael G. Yero and Juan A. Rodr´ıguez-Vel´azquez. Applied Mathematics and Computation 217 (7) (2010) 3571–3574.

13. On global offensive k-alliances in graphs. Sergio Bermudo, Juan A. Rodr´ıguez-Vel´azquez,Ismael G. Yero and Jos´eM. Sigarreta. Applied Mathematics Letters 23 (12) (2010) 1454–1458.

14. On reliability indices of communication networks. Juan Alberto Rodr´ıguez-Vel´azquez,Aida Kamiˇsali´cand Josep Domingo-Ferrer Computers and Mathematics with Applications 58 (7) (2009) 1433–1440.

15. Laplacian eigenvalues and partition problems in hypergraphs. J. A. Rodr´ıguez Applied Mathematics Letters 22 (6) (2009) 916–921.

16. Offensive r-alliances in graphs Henning Fernau, Juan A. Rodr´ıguezand Jos´eM. Sigarreta Discrete Applied Mathematics 157 (1) (2009) 177–182.

17. Defensive k-alliances in graphs Juan A. Rodr´ıguez-Vel´azquez,Ismael G.Yero and Jos´eM. Sigarreta Applied Mathematics Letters 22 (1) (2009) 96–100.

18. Global defensive k-alliances in graphs J. A. Rodr´ıguez-Vel´azquezand J. M. Sigarreta Discrete Applied Mathematics 157 (2) (2009) 211–218. 19. On the global offensive alliance number of a graph J. M. Sigarreta and J. A. Rodr´ıguez Discrete Applied Mathematics 157 (2) (2009) 219–226.

20. Functional centrality in graphs J. A. Rodr´ıguez,E. Estrada and A. Guti´errez Linear and Multilinear Algebra 55 (3) (2007) 293–302.

21. Spectral study of alliances in graphs Juan Alberto Rodr´ıguezVel´azquezand Jos´eMar´ıaSigarreta Almira Discussiones Mathematicae Graph Theory 27 (1) (2007) 143–157.

22. On a graph-spectrum-based structure descriptor I. Gutman, E. Estrada and J. A. Rodr´ıguez-Vel´azquez Croatica Chemica Acta 80 (2) (2007) 151–154.

23. Global alliances in planar graphs J. A. Rodr´ıguez-Vel´azquezand J. M. Sigarreta AKCE–International Journal of Graphs and Combinatorics 4 (1) (2007) 83–98.

24. Offensive alliances in cubic graphs J. A. Rodr´ıguezand J. M. Sigarreta International Mathematical Forum 1 (36) (2006) 1773–1782.

25. The (α, β,s,t)-diameter of graphs: A particular case of conditional diameter J. A. Rodr´ıguez Discrete Applied Mathematics 154 (14) (2006) 2024–2031.

26. Global offensive alliances in graphs J. A. Rodr´ıguez-Vel´azquezand J. M. Sigarreta Electronic Notes in Discrete Mathematics 25 (2006) 157–164.

27. On defensive alliances and line graphs J. M. Sigarreta and J. A. Rodr´ıguez Applied Mathematics Letters 19 (12) (2006) 1345–1350.

28. Subgraph centrality and clustering in complex hyper-networks Ernesto Estrada and Juan A. Rodr´ıguez-Vel´azquez Physica A 364 (2006) 581–594.

29. Atomic branching in molecules Ernesto Estrada, Juan A. Rodr´ıguez-Vel´azquezand Milan Randi´c International Journal of Quantum Chemistry 106 (4) (2006) 823–832. 30. On the Randi´cindex and conditional parameters of a graph J. A Rodr´ıguezand J. M. Sigarreta MATCH Commun. Math. Comput. Chem. 54 (2) (2005) 403–416.

31. A spectral approach to the Randi´cindex J. A. Rodr´ıguez Linear Algebra and its Applications 400 (2005) 339–344.

32. On the Wiener index and the eccentric distance sum of hypergraphs J. A. Rodr´ıguez MATCH Commun. Math. Comput. Chem. 54 (1) (2005) 209–220.

33. Subgraph centrality in complex networks Ernesto Estrada and Juan A. Rodr´ıguez-Vel´azquez Physical Review E 71 (5) 056103 (2005) 9 pages.

34. Spectral measures of bipartivity Ernesto Estrada and Juan A. Rodr´ıguez-Vel´azquez Physical Review E 72 (4) 046105 (2005) 6 pages.

35. On the Laplacian spectrum and walk-regular hypergraphs J. A. Rodr´ıguez Linear and Multilinear Algebra 51 (3) (2003) 285–297.

36. On the Laplacian igenvalues and metric parameters of hypergraphs J. A. Rodr´ıguez Linear and Multilinear Algebra 50 (1) (2002) 1–14.

37. On spectral bounds for cutsets J. A. Rodr´ıguez,A. Guti´errezand J. L. A. Yebra Discrete Mathematics 257 (1) (2002) 101–109.

38. Laplacian eigenvalues and the excess of a graph J. A. Rodr´ıguezand J.L.A. Yebra Ars Combinatoria 64 (2002) 249–258.

39. Bounding the diameter and the mean distance of a graph from its eigenvalues: Laplacian versus adjacency matrix methods J. A. Rodr´ıguezand J.L.A Yebra Discrete Mathematics 196 (1–3) (1999) 267–275. Submitted papers

40. Juan A. Rodr´ıguez,Henning Fernau and Jos´eM. Sigarreta. Powerful r-alliances and total k-domination in graphs. Submitted 2008.

41. Ismael G. Yero, Juan A. Rodr´ıguez-Vel´azquezand Sergio Bermudo. Alliance free sets in Cartesian product graphs. Submitted 2009.

42. Juan A. Rodr´ıguez-Vel´azquez,Ismael G. Yero and Magdalena Lema´nska. On the partition dimension of trees. Submitted 2010.

43. Ismael G. Yero and Juan A. Rodr´ıguez-Vel´azquez,On the Randic’ index of corona product graphs. Submitted 2010.

44. Juan A. Rodr´ıguez-Vel´azquez,Ismael G. Yero and Dorota Kuziak, Partition dimension of corona product graphs. Submitted 2010.

45. Dorota Kuziak, Juan A. Rodr´ıguez-Vel´azquez,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]. Submitted 2010.

46. Ismael G. Yero and Juan A. Rodr´ıguez-Vel´azquez.Analogies between the geodetic number and the Steiner number of some classes of graphs. Submitted 2011.

47. Juan Alberto Rodr´ıguez-Vel´azquez,Ismael G. Yero and Henning Fernau, On the partition dimension of unicyclic graphs. Submitted 2011.

Refereed Conference Publications

• Partition dimension of corona product graphs Juan A. Rodr´ıguez-Vel´azquez,Ismael G. Yero and Dorota Kuziak 7th. Slovenian International Conference on Graph Theory, Bled, Slovenia, 19–25 June 2011. Abstracts 123–124.

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

• On geodetic sets of a graph Sergio Bermudo, Juan A. Rodr´ıguez-Vel´azquez,Jos´eM. Sigarreta and Ismael G. Yero, Colourings, Independence and Domination: 13th Workshop on Graph Theory, CID-2009. September 20-25, 2009, Szklarska Poreba, Poland. Abstracts 86-87.

• Partitioning a graph into offensive k-alliances Jos´eM. Sigarreta, Ismael G. Yero, Sergio Bermudo and Juan A. Rodr´ıguez-Vel´azquez Cologne-Twente Workshop on Graphs and Combinatorial Optimization CTW09, Paris, France. June 2-4, 2009. Abstracts 297-300. • The Laplacian spectrum of hypergraphs J. A. Rodr´ıguez-Vel´azquezand Aida Kamiˇsali´c 15-th Conference of the International Linear Algebra Society, ILAS-2008 Canc´un,M´exico. Abstracts 60-61

• Global r-alliances and total domination H. Fernau, J. A. Rodr´ıguez-Vel´azquezand J. M. Sigarreta Cologne-Twente Workshop on Graphs and Combinatorial Optimization 2008. Universit`a degli Studi di Milano, Gargnano, Italy. Abstracts 98-101

• On the defensive k-alliance number of a graph Juan A. Rodr´ıguez-Vel´azquezand Jos´eM. Sigarreta Cologne-Twente Workshop on Graphs and Combinatorial Optimization 2007. (CTW-2007). University of Twente, Enschede, The Netherlands. Abstracts 133-136, ISBN: 1574-0846

• Mathematical properties of k-Web Communities Juan Alberto Rodr´ıguezVel´azquez,Ismael Gonzalez-Yero and Jos´eMar´ıaSigarreta. INFORMATICA-2007.´ III Taller Internacional de Calidad en las Tecnolog´ıasde la Informa- ci´ony las Comunicaciones. La Habana, Cuba (2007) Proceedings ISBN: 978-959-286-002-5. CAL-019, 9 pages.

• Functional centrality: A centrality measure for social networks analysis Juan A. Rodr´ıguez-Vel´azquezand Cristina Garc´ıa-Moreno COMPUMAT-2007. Holgu´ın,Cuba. Bolet´ınde la Sociedad Cubana de Matem´atica y Computaci´on 5 (N´umeroespecial) MDC9 (2007) 6 pages. ISSN 1728-6042

• Global defensive k-alliances in graphs J. A. Rodr´ıguez-Vel´azquez,J. M. Sigarreta and I. G. Yero COMPUMAT-2007. Holgu´ın,Cuba. Bolet´ınde la Sociedad Cubana de Matem´atica y Computaci´on 5 (N´umeroespecial) MDC8 (2007) 6 pages. ISSN 1728-6042

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

• Global offensive alliances in graphs J. M. Sigarreta and J. A. Rodr´ıguez Cologne-Twente Workshop on Graphs and Combinatorial Optimization 2006. (CTW-2006). Lambrecht, Germany. Abstracts 122-130. • On the degree-adjacency matrix of a graph J. A. Rodr´ıguezand J. M. Sigarreta. 17th International Conference on Formal Power Series and Algebraic Combinatorics. FP- SAC 05. Messina, Italy (2005) Paper N. 41, 14 pages.

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

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

• Uso e integraci´onde las TIC en asignaturas cuantitativas aplicadas. La experiencia de los estudios de inform´aticay multimedia de la UOC. Angel´ A. Juan, Mar´ıaA. Huertas, Cristina Steegmann, Juan A. Rodr´ıguez,Manuel Terradez XI Congreso Universitario de Innovaci´onEducativa en las Ense˜nanzasT´ecnicas (2003) R0184, ISBN 84-688-2216-7

Other Publications

• Cotas de diversos par´ametrosde un grafo a partir de los autovalores de su matriz laplaciana. Juan Alberto Rodr´ıguezVel´azquez Ediciones UPC (1997) ISBN 84-7653-664-X

Editorial work

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

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

Referee for scientific journals

I frequently serve as a referee for scientific journals, including the following:

• Linear and Multilinear Algebra

• Linear Algebra and its Applications

• Discrete Applied Mathematics

• International Journal of Molecular Sciences • Ars Combinatoria

• Australasian Journal of Combinatorics

• Discussiones Mathematicae Graph Theory

• European Journal of Operational Research

• Information Processing Letters

• Applied Mathematics Letters

• Applied Mathematics and Computation

• International Journal of Computer Mathematics

• Hacettepe Journal of Mathematics and Statistics