SOME PROBLEMS IN GRAPH THEORY CONNECTED WITH TOPOLOGY AND ALGEBRA

Problems of the following type are presented:
1. Embedding of in some sense regular graphs into surfaces (of genus greater than 0).
2. Automorphism groups and endomorphism monoids of (finite) graphs:
- different types of endomorphisms;
- algebraic properties of the monoids for specific graphs (trees, bipartite graphs,...).
3. Graph operations:
- categorical interpretation in different categories of graphs;
- graph invariants and graph operations;
- monoids and graph operations.