This research program was at the leading edge of current global trends in the fields of permutation groups, algebraic graph theory and finite geometry. The results obtained allow for a better understanding of many subtle connections between algebraic and combinatorial objects in the perhaps most natural framework of graph theory. Structural results about symmetry properties of mathematical objects has many applications in mathematics as well as outside mathematics (for example in chemistry), and hopefully one day outside science as well. The importance of problems dealt with is best reflected by an extensive bibliography on the subject and many fruitful connections with similar reasearch groups around the world. The main results can be be summarized as follows. 1. Solutions to open problems in algebra, graph theory and finite geometry: If necessary, our success may be measured by publication of a total of 38 original scientific articles in international mathematical journals, 35 of them in the SCI journals, and 4 survey articles. Members of this research group have actively participated at mathematical conferences, giving among other 7 plenary lectures. 2. Posing new problems and opening up new avenues of research in the above mentioned fields: Our past and recent work on symmetry in graphs, covers of graphs and permutation groups, is constantly opening up interesting new questions and has placed members of this research group to the front of recent trends in these area of research in mathematics. 3. Building global connections in the above mentioned research fields: This research group has a long standing cooperation with other similar research groups all over the world, be it in the form of bilateral projects (U.S.A., Israel , P.R. China, Austria, Hungary), or via more informal ties with mathematicians in various other countries, such as: Australia, Canada, New Zealand, England and Slovakia.