Depth and Stanley depth of edge ideals associated to some line graphs

Zahid Iqbal; Muhammad Ishaq; Zahid Iqbal; Muhammad Ishaq

doi:10.3934/math.2019.3.686

AIMS Mathematics

2019, Volume 4, Issue 3: 686-698. doi: 10.3934/math.2019.3.686

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Research article

Depth and Stanley depth of edge ideals associated to some line graphs

Zahid Iqbal ^,,
Muhammad Ishaq

School of Natural Sciences, National University of Sciences and Technology Islamabad, Sector H-12, Islamabad, Pakistan

Received: 21 January 2019 Accepted: 20 May 2019 Published: 19 June 2019
MSC : 13C15, 13P10, 13F20, 05E99

In this paper, we compute some upper and lower bounds for depth and Stanley depth of edge ideals associated to line graphs of the ladder and circular ladder graphs. Furthermore, we determine some bounds for the dimension of the quotient rings of the edge ideals associated to these graphs.
- depth,
- Stanley depth,
- dimension,
- monomial ideal,
- line graph
Citation: Zahid Iqbal, Muhammad Ishaq. Depth and Stanley depth of edge ideals associated to some line graphs[J]. AIMS Mathematics, 2019, 4(3): 686-698. doi: 10.3934/math.2019.3.686

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Abstract

In this paper, we compute some upper and lower bounds for depth and Stanley depth of edge ideals associated to line graphs of the ladder and circular ladder graphs. Furthermore, we determine some bounds for the dimension of the quotient rings of the edge ideals associated to these graphs.

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