THE FORCING HOP DOMINATION NUMBER OF A GRAPH

Let S be a gamma(h)-set of G. A subset T of S is called a forcing subset of S if S is the unique gamma(h)-set containing T. The minimum cardinality of T is the forcing hop domination number of S and is denoted by f gamma(h)(S). The forcing hop domination number of G is f gamma(h)(G) = min{f gamma(h)(G)}, where the minimum is taken over all gamma(h)-sets of G. Some general properties satisfied by this concept are studied. It is shown for every pair a, b of integers with 0 <= a < b and b >= 2, there exists a connected graph G such that f gamma(h)(G) = a and gamma(h)(G) = b, where gamma(h)-set is minimum hop dominating set of G.