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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-18189 |
| Date | 01 January 2010 |
| Creators | Chellali, Mustapha, Haynes, Teresa W., Volkmann, Lutz |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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