Abstract We describe a simple deterministic $$O( \varepsilon ^{-1} \log \Delta )$$ O ( ε - 1 log Δ ) round distributed algorithm for $$(2\alpha +...

Let F1, F2, . . . , Fk be graphs with the same vertex set V . A subset S ⊆ V is a factor dominating set if in every Fi every vertex not in S is adjacent to a vertex in S, and a factor total dominating set if in every Fi every vertex in V is adjacent to a vertex in S. The cardinality of a smallest such set is the factor (total) domination number. We investigate bounds on the factor (total) domin...

Let G be a graph with domination number γ(G). A dominating set S ⊆ V (G) has property UK if all components of the subgraph it induces in G are complete. The union of complete graphs domination number of a graph G, denoted γuk(G), is the minimum possible size of a dominating set of G, which has property UK. Results on changing and unchanging of γuk after vertex removal are presented. Also forbid...