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Paper   IPM / M / 11647
School of Mathematics
  Title:   Bounds for the regularity of edge ideal of vertex decomposable and shellable graphs
1.  S. Moradi
2.  D. Kiani
  Status:   Published
  Journal: Bull. Iranian Math. Soc.
  Vol.:  36
  Year:  2010
  Pages:   267-277
  Supported by:  IPM
n this paper we give upper bounds for the regularity of edge ideal of some classes of graphs in terms of invariants of graph. We introduce two numbers a′(G) and n(G) depending on graph G and show that for a vertex decomposable graph G, \reg(R/I(G)) ≤ min{a′(G),n(G)} and for a shellable graph G, \reg(R/I(G)) ≤ n(G). Moreover it is shown that for a graph G, where Gc is a d-tree, we have \pd(R/I(G))=maxvV(G) {degG(v)}.

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