Graph theory is one of the most applicable fields of mathematics, outside mathematics it is in particular useful in chemistry, molecular biology, bioinformatics and social sciences. The current hot topic of large networks is also based on graph theory. Graph theory is one of the most recognized and established areas of Slovene mathematics, the expression »Slovene graph theory school« became standard in the area. Among the numerous areas of graph theory and related fields we put special emphasize on topological graph theory, structure graph theory, spectral graph theory, metric graph theory, graph products, graph colorings, graph algorithms, computational geometry, combinatorial optimization, Tower of Hanoi problems as well as applications of these areas.

The research group is composed from teams from the University of Ljubljana and the University of Maribor, each having about one half of the members. The research programme is thus very important as it enables fruitful collaboration between the researchers from both universities. The programme in the present form was established in 2004 by merging the programme Graph products and metric graph theory consisting mostly of researchers from the University of Maribor and the programme Topological graph theory with members from the University of Ljubljana.

Our excellence can be proved with top-level publications, numerous invited talks at conferences and universities as well as with our editorial work in central, even prestigious, journals from the area of graph theory and more generally discrete mathematics. Another important achievement are four books published by leading scientific publishers. The first two, »Product graphs: Structure and Recognition«, published in 2000 by Wiley-Interscience and »Graphs on Surfaces« from 2001, published by Johns Hopkins University Press, are among the most cited works of Slovenian mathematics. They were follows with two more books published in 2008 and 2011 with A K Peters and CRC Press, respectively.