Geodesic
On the ρ-Edge Stability Number of Graphs
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 249-262

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For an arbitrary invariant ρ(G) of a graph G the ρ-edge stability number es_ρ (G) is the minimum number of edges of G whose removal results in a graph H ⊆ G with ρ (H) 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 es_χ^′ (G) and determine es_χ^′ (G) exactly for specific classes of graphs.
Keywords: edge stability number, line stability, invariant, chromatic edge stability index, chromatic index, edge coloring 
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Kemnitz, Arnfried; Marangio, Massimiliano. On the ρ-Edge Stability Number of Graphs. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 249-262. http://geodesic.mathdoc.fr/item/DMGT_2022_42_1_a15/