Geodesic
On the ρ-Edge Stability Number of Graphs
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 1, pp. 249-262 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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 
@article{DMGT_2022_42_1_a15,
     author = {Kemnitz, Arnfried and Marangio, Massimiliano},
     title = {On the {\ensuremath{\rho}-Edge} {Stability} {Number} of {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {249--262},
     year = {2022},
     volume = {42},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2022_42_1_a15/}
}
TY  - JOUR
AU  - Kemnitz, Arnfried
AU  - Marangio, Massimiliano
TI  - On the ρ-Edge Stability Number of Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2022
SP  - 249
EP  - 262
VL  - 42
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGT_2022_42_1_a15/
LA  - en
ID  - DMGT_2022_42_1_a15
ER  - 
%0 Journal Article
%A Kemnitz, Arnfried
%A Marangio, Massimiliano
%T On the ρ-Edge Stability Number of Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2022
%P 249-262
%V 42
%N 1
%U http://geodesic.mathdoc.fr/item/DMGT_2022_42_1_a15/
%G en
%F DMGT_2022_42_1_a15
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/

[1] S. Arumugam, I. Sahul Hamid and A. Muthukamatchi, Independent domination and graph colorings, Ramanujan Math. Soc. Lect. Notes Ser. 7 (2008) 195–203.

[2] D. Bauer, F. Harary, J. Nieminen and C.L. Su el, Domination alteration sets in graphs, Discrete Math. 47 (1983) 153–161. https://doi.org/10.1016/0012-365X(83)90085-7

[3] A. Kemnitz, M. Marangio and N. Movarraei, On the chromatic edge stability number of graphs, Graphs Combin. 34 (2018) 1539–1551. https://doi.org/10.1007/s00373-018-1972-y

[4] M. Plantholt, The chromatic index of graphs with a spanning star, J. Graph Theory 5 (1981) 45–53. https://doi.org/10.1002/jgt.3190050103

[5] W. Staton, Edge deletions and the chromatic number, Ars Combin. 10 (1980) 103–106.

[6] J.-M. Xu, On bondage numbers of graphs: A survey with some comments, Int. J. Comb. 2013 (2013) ID 595210. https://doi.org/10.1155/2013/595210