On the \rho-edge stability number of graphs

For an arbitrary invariant ρ(G) of a graph G the ρ-edge stability number esρ(G) is the minimum number of edges of G whose removal results in a graph H ⊆ G with ρ(H) 6= ρ(G) or with E(H) = ∅. In the first part of this paper we give some general lower and upper bounds for the ρ-edge stability number. In the second part we study the χ′edge stability number of graphs, where χ′ = χ′(G) is the chromatic index of G. We prove some general results for the so-called chromatic edge stability index esχ′(G) and determine esχ′(G) exactly for specific classes of graphs.