Title

Certain algebraic invariants of edge ideals of join of graphs.

Authors

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.

Subjects

COMPLETE graphs; POWER (Social sciences); EDGES (Geometry)

Publication

Journal of Algebra & Its Applications, 2021, Vol 20, Issue 6, pN.PAG

ISSN

0219-4988

Publication type

Academic Journal

DOI

10.1142/S0219498821500997