We introduce a new concept of strong domination and connected strong domination in hypergraphs. The relationships between strong domination number and other hypergraph parameters like domination, independence, strong independence and irredundant numbers of hypergraphs are considered. There are also some chains of inequalities generalizing the famous Cockayne, Hedetniemi and Miller chain for parameters of graphs. There are given some generalizations of well known theorems for graphs, namely Gallai type theorem generalizing Nieminen, Hedetniemi and Laskar theorems.
1970-2025 CP (Manitoba, Canada) unless otherwise stated.