Dominating induced matchings of finite graphs and regularity of edge   ideals
  The regularity of an edge ideal of a finite simple graph $G$ is at least the induced matching number of $G$ and is at most the minimum matching number of $G$. If $G$ possesses a dominating inuduced matching, i.e., an induced matching which forms a maximal matching, then the induced matching number of $G$ is equal to the minimum matching number of $G$. In the present paper, from viewpoints of both combinatorics and commutative algebra, finite simple graphs with dominating induced matchings will be mainly studied. 
Takayuki Hibi, Akihiro Higashitani, Kyouko Kimura, Akiyoshi Tsuchiya
math.CO math.AC