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Certain algebraic invariants of edge ideals of join of graphs
Date Issued
01-06-2021
Author(s)
Kumar, Arvind
Kumar, Rajiv
Sarkar, Rajib
Abstract
Let G be a simple graph and I(G) be its edge ideal. In this paper, we study the Castelnuovo-Mumford regularity of symbolic powers of edge ideals of join of graphs. As a consequence, we prove Minh's conjecture for wheel graphs, complete multipartite graphs, and a subclass of co-chordal graphs. We obtain a class of graphs whose edge ideals have regularity three. By constructing graphs, we prove that the multiplicity of edge ideals of graphs is independent from the depth, dimension, regularity, and degree of h-polynomial. Also, we demonstrate that the depth of edge ideals of graphs is independent from the regularity and degree of h-polynomial by constructing graphs.
Volume
20