The software GADAR and its application to extremal graph theory For the class of algebraically defined graphs -- i.e., graphs in which adjacency between vertices is defined by some algebraic relations -- existing software packages turned out to be too inefficient. GADAR (short for “Graphs with Algebraically Defined Adjacency Relations”) is a package based on Mathematica. For its design and implementation techniques of object-oriented programming were used. The package is applied to investigation of the infinite families of graphs ${cal D}_{k,q}$ and ${cal C} D_{k,q}$ for which some non-intuitive conjectures were obtained. As Lazebnik, Ustimenko and Woldar could prove, the family ${cal C} D_{k,q}$ is an example of a family of graphs which for given order and girth have the largest size (with a finite number of exceptions).

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