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.