Suppose V is a finite set and C a collection of subsets of V that contains ∅ and V and is closed under taking intersections. Then the ordered pair (V, C) is called a convexity and the elements of C are referred to as convex sets. For a set S ⊆ V , the convex hull of S relative to C, denoted by CHC(S), is the smallest convex set containing S. The Caratheodory number, relative to a given convexit...

The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2) enumeration barri...

The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2) enumeration barri...

The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a long-standing open question whether determining these numbers for a graph G on n vertices admits exact algorithms running in time less than the trivial Ω(2) enumeration barri...

The domination number γ(G) of the fuzzy graph G is the minimum cardinality taken over all minimal dominating sets of G. The independent domination number i(G) is the minimum cardinality taken over all maximal independent sets of G. The irredundant number ir(G) is the minimum cardinality taken over all maximal irredundant sets of G. In this paper we prove the result that relate the parameters ir...

During the last thirty years, the concept of domination in graphs has generated an impressive interest. A recent bibliography on the subject contains more than 1200 references and the number of new definitions is continually increasing. Rather than trying to give a catalogue of all of them, we survey the most classical and important notions (as independent domination, irredundant domination, k-...