Bounds for the regularity of edge ideal of vertex decomposable and shellable graphs

Author(s):

S. Moradi , D. Kiani

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)) min{a0(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)) = maxv2V (G){degG(v)}.
Language:
English
Published:
Bulletin of Iranian Mathematical Society, Volume:36 Issue: 2, 2010
Page:
267
https://www.magiran.com/p807289