This special volume contains a selection of papers presented at the conference "Recent Trends in Graph Theory, Algebraic Combinatorics, and Graph Algorithms" held in Bled, Slovenia, September 24-27, 2001. The conference was dedicated to Wilfried Imrich for his contributions to the development of Graph Theory in Slovenia on the occasion of his sixtieth birthday. There were 58 participants at the conference, 26 from Slovenia, while the others came from 13 different countries (Austria, Czech Republic, France, Italy, Israel, Canada, Hungary, Germany, The Netherlands, New Zealand, Russia, Sweden, USA). 47 talks were presented during the meeting.

Graph Theory meetings have a long tradition in Slovenia. A series of four "Slovenian International Conferences in Graph Theory" were held in 1985, 1991, 1995, and 1999. The fifth conference in the series is planned for 2003. In parallel, in the early 1980s graph theory groups from Ljubljana and Leoben started a series of meetings that is now called the "Leoben-Ljubljana Seminar on Discrete Mathematics". At the first meeting there were only six participants: Vladimir Batagelj, Wilfried Imrich, Bojan Mohar, Tomaz Pisanski, Norbert Seifter, and Wolfgang Woess. Since 1989 the meetings have an official program, the latest meeting "19th LL Seminar on Graph Theory" took place in Vienna, April 25-28, 2002.

As we already mentioned, the present conference honored Wilfried Imrich's contributions to the development of Graph Theory in Slovenia. Together with Tomaz Pisanski he was the founder of the above mentioned LL-seminar. This act was of utmost importance for the long lasting cooperation between the graph theorists in Slovenia and Austria. Too many connections and collaborations arose in these 20 years to be mentioned here. As examples we just mention that Wilfried and Tomo are academic fathers of Sandi Klavžar and Janez Zerovnik; that Norbert Seifter closely collaborates with Dragan Marusic, Aleksander Malnic and Boris Zgrablić on automorphism groups of graphs; Wolfgang Woess and Bojan Mohar are co-authors of a nice survey on spectra of infinite graphs; and Wilfried together with Sandi Klavžar published the book "Product Graphs: Structure and Recognition". The present conference can thus be understood as the highlight of the 20 years of the LL-meetings.

The organizers thank the authors for their contributions, the referees for their careful work, the Slovenian Ministry of Education, Science and Sport for financial assistance of the conference, and the Institute of Mathematics, Physics and Mechanics for financial and technical support of the conference. We also wish to thank Mieczys aw Borowiecki, Editor-in-Chief of Discussiones Mathematicae Graph Theory, for enabling this issue to appear, and Danuta Michalak for her permanent help.

Ljubljana, Maribor, Leoben, July 2002

Sandi Klavžar, Bojan Mohar, Tomaz Pisanski,
Norbert Seifter, Janez Zerovnik