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 sub-graph of G containing W. S(W) denotes the set of vertices that lies in Steiner W-trees. Steiner set of a graph was introduced by Chartrand and Zhang (2002). An edge Steiner set of a graph was introduced by Santhakumaran and John (2007). In this paper, we introduce edge fixed edge Steiner set and study some of the characteristics of edge fixed edge Steiner number and provide the bounds for edge fixed edge Steiner number. Also we prove the existence theorem.
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