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arXiv · 2204.05489

Symbolic defects of edge ideals of unicyclic graphs

Mousumi Mandal·Dipak Kumar Pradhan
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Abstract

We introduce the concept of minimum edge cover for an induced subgraph in a graph. Let $G$ be a unicyclic graph with a unique odd cycle and $I=I(G)$ be its edge ideal. We compute the exact values of all symbolic defects of $I$ using the concept of minimum edge cover for an induced subgraph in a graph. We describe one method to find the quasi-polynomial associated with the symbolic defects of edge ideal $I$. We classify the class of unicyclic graphs when some power of maximal ideal annihilates $ I^{(s)}/I^s $ for any fixed $ s $. Also for those class of graphs, we compute the Hilbert function of the module $I^{(s)}/I^s$ for all $s.$

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Mousumi Mandal, Dipak Kumar Pradhan. 2022-04-12. Symbolic defects of edge ideals of unicyclic graphs. https://doi.org/10.1142/s0219498823500998

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