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Results in Mathematics

, 74:140 | Cite as

Normality of Cover Ideals of Graphs and Normality Under Some Operations

  • Ibrahim Al-AyyoubEmail author
  • Mehrdad Nasernejad
  • Leslie G. Roberts
Article
  • 56 Downloads

Abstract

We produce a procedure for constructing new normal monomial ideals from other ideals that are assumed to be normal. This enables us to prove that if the cover ideal of a graph G is normal, then the cover ideal of the graph H is normal as well, where the graph H is obtained by connecting all vertices in G with a new vertex. We use these ideas to explore the normality of the cover ideals of some imperfect graphs. Also, we investigate the normality under expansion, this leads us to generalize the work of Al-Ayyoub (Rocky Mountain J Math 39:1–9, 2009). Furthermore, we investigate the normality under more operations such as weighting, polarization, localization, contraction, and deletion.

Keywords

Normal ideals cover ideals monomial operators imperfect graphs 

Mathematics Subject Classification

13B22 05C25 05E40 

Notes

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Copyright information

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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsJordan University of Science and TechnologyIrbidJordan
  2. 2.Department of MathematicsKhayyam UniversityMashhadIran
  3. 3.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada

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