Regularity and projective dimension of the edge ideal of ₅-free vertex decomposable graphs

  title={Regularity and projective dimension of the edge ideal of ₅-free vertex decomposable graphs},
  author={F. Khosh-Ahang and S. Moradi},
  • F. Khosh-Ahang, S. Moradi
  • Published 2014
  • Mathematics
  • In this paper, we explain the regularity, projective dimension and depth of edge ideal of some classes of graphs in terms of invariants of graphs. We show that for a C5-free vertex decomposable graph G, reg(R/I(G)) = cG, where cG is the maximum number of 3-disjoint edges in G. Moreover for this class of graphs we characterize pd(R/I(G)) and depth(R/I(G)). As a corollary we describe these invariants in forests and sequentially CohenMacaulay bipartite graphs. 
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