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2017 Algebraic properties of spanning simplicial complexes
Fahimeh Khosh-Ahang, Somayeh Moradi
Rocky Mountain J. Math. 47(6): 1901-1916 (2017). DOI: 10.1216/RMJ-2017-47-6-1901

Abstract

In this paper, we study some algebraic properties of the spanning simplicial complex $\Delta _s(G)$ associated to a multigraph~$G$. It is proved that, for any finite multi\-graph~$G$, $\Delta _s(G)$ is a pure vertex decomposable simplicial complex and therefore shellable and Cohen-Macaulay. As a consequence, we deduce that, for any multigraph~$G$, the quotient ring $R/I_c(G)$ is Cohen-Macaulay, where \[ I_c(G)=(x_{i_1} \cdots x_{i_k} \mid \{x_{i_1},\ldots , x_{i_k}\}\qquad \qquad \qquad \] \[ \qquad \qquad \qquad \mbox {is the edge set of a cycle in~$G$}). \] Also, some homological invariants of the Stanley-Reisner ring of $\Delta _s(G)$, such as projective dimension and regularity, are investigated.

Citation

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Fahimeh Khosh-Ahang. Somayeh Moradi. "Algebraic properties of spanning simplicial complexes." Rocky Mountain J. Math. 47 (6) 1901 - 1916, 2017. https://doi.org/10.1216/RMJ-2017-47-6-1901

Information

Published: 2017
First available in Project Euclid: 21 November 2017

zbMATH: 06816575
MathSciNet: MR3725249
Digital Object Identifier: 10.1216/RMJ-2017-47-6-1901

Subjects:
Primary: 13D02, 13P10
Secondary: 16E0

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 6 • 2017
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