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Paper   IPM / M / 17152
School of Mathematics
  Title:   Hankel edge ideals of trees and (semi-)Hamiltonian graphs
  Author(s):  Sara Saeidi madan (Joint with D. Kiani and S. Tafazolian)
  Status:   Published
  Journal: Bull. Malaysian Math. Soc.
  Vol.:  45
  Year:  2022
  Pages:   2493-2507
  Supported by:  IPM
In this paper, we study the Hankel edge ideals of graphs. We determine the minimal prime ideals of the Hankel edge ideal of labeled Hamiltonian and semi-Hamiltonian graphs, and we investigate radicality, being a complete intersection, almost complete intersection and set-theoretic complete intersection for such graphs. We also consider the Hankel edge ideal of trees with a natural labeling, called rooted labeling. We characterize such trees whose Hankel edge ideal is a complete intersection, and moreover, we determine those whose initial ideal with respect to the reverse lexicographic order satisfies this property.

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