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On the maximum number of maximum independent sets in connected graphs
Journal of Graph Theory ( IF 0.9 ) Pub Date : 2020-10-11 , DOI: 10.1002/jgt.22629
Elena Mohr 1 , Dieter Rautenbach 1
Affiliation  

We characterize the connected graphs of given order n and given independence number α that maximize the number of maximum independent sets. For 3 α n 2 , there is a unique such graph that arises from the disjoint union of α cliques of orders n α and n α , which is the complement of a Turán graph, by selecting a vertex x in a largest clique and adding an edge between x and a vertex in each of the remaining α 1 cliques. Our result confirms a conjecture of Derikvand and Oboudi.

中文翻译:

关于连通图中最大独立集的最大数目

我们刻画给定顺序的连通图 ñ 并给出独立编号 α 最大化最大独立集的数量。为了 3 α ñ 2 ,有一个独特的图是由 α 订单集团 ñ α ñ α ,这是Turán图的补码,方法是选择一个顶点 X 在最大的集团中并在 X 其余各有一个顶点 α - 1个 集团。我们的结果证实了Derikvand和Oboudi的猜想。
更新日期:2020-10-11
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