The second largest number of maximal independent sets in connected graphs with at most one cycle

The second largest number of maximal independent sets in connected graphs with at most one cycle

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Article ID: iaor20125700
Volume: 24
Issue: 3
Start Page Number: 192
End Page Number: 201
Publication Date: Oct 2012
Journal: Journal of Combinatorial Optimization
Authors:
Keywords: graphs
Abstract:

A maximal independent set is an independent set that is not a proper subset of any other independent set. In this paper, we determine the second largest number of maximal independent sets among all graphs (respectively, connected graphs) of order n≥4 with at most one cycle. We also characterize those extremal graphs achieving these values.

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