Abstract
For a non - empty set W of vertices in a connected graph G, the steiner distance d(W) of W is the minimum size of a connected subgraph G containing W. Necessarily, each such subgraph is a tree and is called a steiner tree or a steiner W - tree. The set of all vertices of G that lie on some steiner W - tree is denoted by S(W). If S(W) = V (G) then W is called a steiner set for G. The steiner number s(G) is the minimum cardinality of a steiner set. The minimum cardinality of a steiner dominating set is called the steiner domination number of graph.
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