The ∘ operation and * operation of Cohen-Macaulay bipartite graphs

2023/09/24 by Yulong Yang, Guangjun Zhu, Yang, Yulong +5
Mathematics · Medicine · #13A15 #13D02 #Cholinesterase and Neurodegenerative Diseases #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Primary 13C15 #Secondary 05E40

paper · pdf · doi:10.48550/arxiv.2309.13568

openalex publication_date 2023/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite simple graph with the vertex set V and let I_G be its edge ideal in the polynomial ring S=\mathbbK[x_V]. In this paper, we compute the depth and the Castelnuovo--Mumford regularity of S/I_G when G=G₁∘ G₂ or G=G₁* G₂ is a graph obtained from Cohen-Macaulay bipartite graphs G₁, G₂ by ∘ operation or * operation, respectively.

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