Quantum graphs and their characteristics are intriguing generalizations of notions and tools known from discrete mathematics into the quantum world. Their non-trivial relations with quantum information theory provide a bridge between this branch of mathematics and quantum mechanics. In classical graph theory, there are several characteristics that one can associate with given graphs, e.g., chromatic or clique numbers. The famous problem, solved by Mycielski, was to construct a graph that contains a given graph as a subgraph and can have an arbitrarily large chromatic number, but no larger clique is produced. We propose an analog of the Mycielski transformation and its generalizations in the quantum setting and study how they affect the (quantum) characteristics of quantum graphs. Moreover we study relations between quantum automorphism groups of a quantum graph and its Mycielskian. Based on joint work with A. Bochniak (arXiv:2306.09994) and work in progress with A. Bochniak, P.M. Sołtan, and I. Chełstowski.