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Mathematics 2016, 4(3), 43; doi:10.3390/math4030043

Cohen Macaulayness and Arithmetical Rank of Generalized Theta Graphs

Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Ave., P.O. Box 15875-4413, Tehran 1591634311, Iran
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Academic Editor: Hvedri Inassaridze
Received: 5 March 2016 / Revised: 5 June 2016 / Accepted: 6 June 2016 / Published: 29 June 2016
(This article belongs to the Special Issue Homological and Homotopical Algebra and Category Theory)
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Abstract

In this paper, we study some algebraic invariants of the edge ideal of generalized theta graphs, such as arithmetical rank, big height and height. We give an upper bound for the difference between the arithmetical rank and big height. Moreover, all Cohen-Macaulay (and unmixed) graphs of this type will be characterized. View Full-Text
Keywords: arithmetical rank; Cohen-Macaulay; height arithmetical rank; Cohen-Macaulay; height
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Seyyedi, S.M.; Rahmati, F. Cohen Macaulayness and Arithmetical Rank of Generalized Theta Graphs. Mathematics 2016, 4, 43.

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