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arXiv · 2107.05874

Minimum Generating Sets for Complete Graphs

Selma Altınok·Gökçen Dilaver
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Abstract

Let $G$ be a graph whose edges are labeled by ideals of a commutative ring $R$ with identity. Such a graph is called an edge-labeled graph over $R$. A generalized spline is a vertex labeling so that the difference between the labels of any two adjacent vertices lies in the ideal corresponding to the edge. These generalized splines form a module over $R$. In this paper, we consider complete graphs whose edges are labeled with proper ideals of $\mathbb{Z} / m\mathbb{Z}$. We compute minimum generating sets of constant flow-up classes for spline modules on edge-labeled complete graphs over $\mathbb{Z} / m\mathbb{Z}$ and their rank under some restrictions.

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Selma Altınok, Gökçen Dilaver. 2022-01-20. Minimum Generating Sets for Complete Graphs. https://arxiv.org/abs/2107.05874

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