Maximal independent sets in bipartite graphs with at least one cycle
نویسندگان
چکیده
A maximal independent set is an independent set that is not a proper subset of any other independent set. Liu [J.Q. Liu, Maximal independent sets of bipartite graphs, J. Graph Theory, 17 (4) (1993) 495-507] determined the largest number of maximal independent sets among all n-vertex bipartite graphs. The corresponding extremal graphs are forests. It is natural and interesting for us to consider this problem on bipartite graphs with cycles. Let Bn (resp. B n) be the set of all n-vertex bipartite graphs with at least one cycle for even (resp. odd) n. In this paper, the largest number of maximal independent sets of graphs in Bn (resp. B n) is considered. Among Bn the disconnected graphs with the first-, second-, . . . , n−2 2 -th largest number of maximal independent sets are characterized, while the connected graphs in Bn having the largest and the second largest number of maximal independent sets are determined. Among
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عنوان ژورنال:
- Discrete Mathematics & Theoretical Computer Science
دوره 15 شماره
صفحات -
تاریخ انتشار 2013