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arXiv · 2511.22953

Algebraic study on rooted products of graphs and multi-clique corona graphs

Yuji Muta·Naoki Terai
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Abstract

In this paper, we study rooted products of graphs from the perspective of combinatorial commutative algebra. For edge ideals, we introduce the 2-Cohen-Macaulayness with respect to a vertex and use it to investigate when edge ideals of rooted products of graphs are Cohen-Macaulay. Moreover, we completely determine when attaching a graph on at most six vertices to a given graph as rooted products, yields a Cohen-Macaulay edge ideal. Also, we define mulit-clique corona graphs as a generalization of clique-corona graphs and multi-whisker graphs. We prove that multi-clique corona graphs are vertex decomposable and hence sequentially Cohen-Macaulay. Also, we give formulas for the projective dimension and the Castelnuovo-Mumford regularity.

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Yuji Muta, Naoki Terai. 2025-11-28. Algebraic study on rooted products of graphs and multi-clique corona graphs. https://arxiv.org/abs/2511.22953

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