I am Professor of Applied Mathematics at the Universitat Politècnica de Catalunya and I am member of the research group “Combinatorics, Graph Theory and Applications” of this university. I am interested in the application of graph theory to the design of topologies and communication strategies for interconnection networks, with special emphasis on the study of connectivity problems in graphs and digraphs. In this line of research I have proven some nice characterizations of maximally connected graphs and digraphs. I am also co-author of the chapters of the “Handbook of Graph Theory” devoted to graph connectivity. My research subjects also target the spectral characterization of topological properties of interconnection networks. I have directed and co-directed eight doctoral theses.
- Connectivity of graphs and digraphs
- Spectral graph theory
- Algorithms in graphs
- Combinatorics and discrete mathematics
- M.C. Balbuena, J. Fàbrega, X. Marcote and I. Pelayo, Superconnected digraphs and graphs with small conditional diameters, Networks, vol. 39 no. 3 (2002), pp. 153–160.
- M. Cámara, J. Fàbrega, M.A. Fiol and E. Garriga, Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes, Electronic Journal of Combinatorics, 16(1) (2009), \#R83 , Jul. 2009.
- J. Gómez, J. Fàbrega and J.L.A. Yebra, On large (Δ, D, D, 1)-graphs, Networks, vol. 57 no. 4 (2011), pp. 316–327.
- M. Cámara, C. Dalfó, J. Fàbrega, M.A. Fiol and E. Garriga, Edge-distance-regular graphs,Journal of Combinatorial Theory Ser. A, vol. 118 no. 7 (2011), pp. 2071—2091.
- C. Balbuena, J. Fàbrega and M.A. Fiol, Connectivity: Properties and Structure, Handbook of Graph Theory, Second Edition, Section 4.1, pp 234—257, ed. by J.L. Groos, J. Yellen and P. Zhang, CRC Press 2013, ISBN: 978-1-4398-8018-0.