Abstract
AbstractIn 2004, Biedl et al proved that if is a connected cubic graph of order , then , where is the matching number of . The graphs achieving equality in this bound were characterized in 2010 by O and West. In 2017, Haxell and Scott proved that if is a connected subcubic graph, then , where denotes the number of vertices of degree in . In this paper, we characterize the graphs achieving equality in the lower bound on the matching number given by Haxell and Scott.
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