Algebraic Methods in Graph Theory Approved by: Programa PESSOA 2005/GRICES Dates: January 2005 - December 2006 Coordinators: D. Forge and D. M. Cardoso Research team: French researchers: C. Delorme, P. Bertholomé, D. Forge and M. Kouider from University of Paris-Sud. Portuguese researchers: D. M. Cardoso and P. Rama from University of Aveiro; J. O. Cerdeira and R. Cordovil from Technical University of Lisbon. Research topics: Spectral properties of matrices of graphs with a (k,p)-regular set (vertex subset S inducing a k-regular subgraph such that each vertex out of S has p neighbours in S) and their combinatorial applications. Graph orientations using oriented matroids. Applications of graph theory to the preservation of ecosystems. Topological and combinatorial study of simplicial complexes and its simplicial homology. Research visits supported by the project: R. Cordovil, University of Paris-Sud, Orsay (LRI), 1 - 30 June 2005. C. Delorme, University of Aveiro, Maths Department (CEOC), 6-13 July 2005. (Details and photos) D. Forge, IST, 5-24 September 2005. J. O. Cerdeira, University of Paris-Sud, Orsay, 24 November to 5 December 2005. Scientific Report in Portuguese