My principal areas of research concern some connections between general algebra, number theory and combinatorics. The research concerns also graph theory, in particular algorithms for edge weightings and vertex colorings of graphs.
Problems:
1) Algebraic realization of closure operators
2) Matroids and incidence structures
3) n-modularity and n-distributivity properties in lattices
4) Properties of digraphs connected with some congurence relations
5) Properties of the zero-divisor graph of the ring Zn
6) Multiplicative vertex-colouring edge-weightings of graphs (1-2-3 Conjecture in multiplicative version)
7) Multiset 1-2-3 Conjecture for graphs
8) Multiplicative vertex-colouring proper edge-weightings of graphs (neighbor product distinguishing index for some classes of graphs)
9) Total weightings of graphs and 1-2 Conjecture in multiplicative version
10) Multiplicative 1-2-3 Conjecture and 1-2 Conjecture for hypergraphs
11) Multiplicative vertex-coloring lucky labelings of vertices of graphs.