The edge-to-vertex Steiner domination number of a graph

Abstract

A set W ? E is said to be an edge-to-vertex Steiner dominating set of G if W is both an edge-to-vertex dominating set and a edge-to-vertex Steiner set of G. The edge-to-vertex Steiner domination number ?sev(G) of G is the minimum cardinality of its edge-to-vertex Steiner dominating set of G and any edge-to-vertex Steiner dominating set of cardinality ?sev(G) is a ?sev-set of G. Some general properties satisfied by this concept are studied. The edge-to-vertex Steiner domination number of certain classes of graphs are determined. Connected graph of size q ? 3 with edge-to-vertex Steiner domination number q or q ?1 are characterized. It is shown for every pair a, b of integers with 2 ? a ? b, there exists a connected graph G such that ?ev(G) = a and ?sev(G) = b.