The edge geodetic fault tolerant domination number of a graph

For a connected graph G = (V, E), a set F⊆V is said to be an edge geodetic fault tolerant dominating set of G if F is both edge geodetic set and fault tolerant dominating set of G. The minimum cardinality of an edge geodetic fault tolerant dominating set of G is called the edge geodetic fault tolerant domination number of G and is denoted by γgeft(G). The edge geodetic fault tolerant domination number of certain classes of graphs are determined. It is shown that for each pair of integers 3 ≤a < b, there exists a connected graph G such that γ(G) = a, γge (G)= b and γgeft(G) = a + b-1, where γ(G), ge γ(G) and γgeft(G) are the domination number, edge geodetic domination number and edge geodetic fault tolerant domination number of G respectively.