Automatic graph generation for e-learning systems

The subject of the research is one of the ways of updating modern training systems for solving problems of graph theory, namely, automatic generation of graphs. This approach will reduce the load on the training system database and generate tasks for the user in real-time without updating the bank of tasks. In the course of the work, the advantages and disadvantages of this approach were identified. The most suitable method for the implementation of the research was chosen to represent graphs in electronic computers. The requirements for generated graphs and possible ways of implementing these requirements are identified and substantiated. Namely: in the implemented program, simple connected undirected graphs will be generated. We considered an important detail in working with graphs - graph traversal using the “Depth (width) search” algorithm, which in this task is used to check the graph for connectivity. The result of the work is presented - a software implementation of the graph generation algorithm in the C# programming language. In it, graphs are represented by an adjacency list, generated randomly, and checked for connectivity using the DFS (Depth First Search) function. DFS is a software implementation of the Depth First Search algorithm.