## Graph Operations Preserving W2-Property

- Vadim E. Levit, Eugen Mandrescu
- Electronic Notes in Discrete Mathematics
- 2018

@article{Levit2017W2graphsAS, title={W2-graphs and shedding vertices}, author={Vadim E. Levit and Eugen Mandrescu}, journal={Electronic Notes in Discrete Mathematics}, year={2017}, volume={61}, pages={797-803} }

- Published 2017 in Electronic Notes in Discrete Mathematics
DOI:10.1016/j.endm.2017.07.038

A graph is well-covered if all its maximal independent sets are of the same size (Plummer, 1970). A well-covered graph is 1-well-covered if the deletion of every vertex leaves a graph which is well-covered as well (Staples, 1975). A graph G belongs to class Wn if every n pairwise disjoint independent sets in G are included in n pairwise disjoint maximum independent sets (Staples, 1975). Clearly, W1 is the family of all well-covered graphs. It turns out that G ∈ W2 if and only if it is a 1-well… CONTINUE READING