K-Independence Stable Graphs Upon Edge Removal
Document Type
Article
Publication Date
1-1-2010
Description
Let k be a positive integer and G = (V (G),E(G)) a graph. A subset S of V (G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k-1. The maximum cardinality of a k-independent set of G is the k-independence number βk(G). A graph G is called βk- -stable if βk(G - e) = βk(G) for every edge e of E(G). First we give a necessary and sufficient condition for βk--stable graphs. Then we establish four equivalent conditions for βk--stable trees.
Citation Information
Chellali, Mustapha; Haynes, Teresa W.; and Volkmann, Lutz. 2010. K-Independence Stable Graphs Upon Edge Removal. Discussiones Mathematicae - Graph Theory. Vol.30(2). 265-274. https://doi.org/10.7151/dmgt.1492 ISSN: 1234-3099