A Note on the Maximum Number of Minimal Connected Dominating Sets in a Graph

11/11/2021

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by   Faisal N. Abu-Khzam, et al.

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We prove constructively that the maximum possible number of minimal connected dominating sets in a connected undirected graph of order n is in Ω(1.489^n). This improves the previously known lower bound of Ω(1.4422^n) and reduces the gap between lower and upper bounds for input-sensitive enumeration of minimal connected dominating sets in general graphs as well as some special graph classes.