Title of article
Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs
Author/Authors
MORADI, S. Institute for Research in Fundamental Sciences (IPM) - School of Mathematics, ايران , MORADI, S. ilam university - Department of Mathematics, ايلام, ايران , KIANI, D. amirkabir university of technology - Faculty of Mathematics and Computer Science - Department of Pure Mathematics, تهران, ايران , KIANI, D. Institute for Research in Fundamental Sciences (IPM) - School of Mathematics, ايران
From page
267
To page
277
Abstract
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 a0(G) and n(G) depending on graph G and show that for a vertex decomposable graph G, reg(R/I(G)) leq min{a (G), n(G)} and for a shellable graph G, reg(R/I(G)) leq n(G). Moreover, it is shown that for a graph G, where Gc is a d-tree, we have pd(R/I(G)) = maxv2V (G){degG(v)}
Keywords
Edge ideals , vertex decomposable , shellable complex , Castelnuovo , Mumford regularity , projective dimension
Journal title
Bulletin of the Iranian Mathematical Society
Journal title
Bulletin of the Iranian Mathematical Society
Record number
2549404
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