On the Number of k-Dominating Independent Sets
نویسنده
چکیده
We study the existence and the number of k-dominating independent sets in certain graph families. While the case k = 1 namely the case of maximal independent sets which is originated from Erdős and Moser is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of kdominating independent sets in n-vertex graphs is between ck · 2k √ 2 n and ck · k+1 √ 2 n if k ≥ 2, moreover the maximum number of 2-dominating independent sets in n-vertex graphs is between c · 1.22 and c′ · 1.246. Graph constructions containing a large number of kdominating independent sets are coming from product graphs, complete bipartite graphs and finite geometries. The product graph construction is associated with the number of certain MDS codes.
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 84 شماره
صفحات -
تاریخ انتشار 2017