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arXiv · 1801.01975

A construction of sequentially Cohen-Macaulay graphs

A-Ming Liu·Tongsuo Wu
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Abstract

For every simple graph $G$, a class of multiple clique cluster-whiskered graphs $G^{md}$ is introduced, and it is shown that all graphs $G^{md}$ are vertex decomposable, thus the independence simplicial complex ${\rm Ind}\,G^{md}$ is sequentially Cohen-Macaulay; the properties of the graphs $G^{md}$ and the clique-whiskered graph $G^\pi$ are studied, including the enumeration of facets of the complex ${\rm Ind}\, G^{\pi}$ and, the calculation of Betti numbers of the cover ideal $I_c(G^{md})$.

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A-Ming Liu, Tongsuo Wu. 2018-01-06. A construction of sequentially Cohen-Macaulay graphs. https://arxiv.org/abs/1801.01975

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