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
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
