The ∘ operation and * operation of fan graphs

2023/08/11 by Guangjun Zhu, Zhu, Guangjun, Yijun Cui +5
Computer Science · Mathematics · #13A15 #13D02 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13C15 #Secondary 05E40

paper · pdf · doi:10.48550/arxiv.2308.06010

openalex publication_date 2023/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite simple graph on the vertex set V and let I_G denote 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=F_k^W(K_n) is a k-fan graph, or G=G₁∘ G₂ or G=G₁* G₂ is the graph obtained from fan graphs G₁, G₂ by ∘ operation or * operation, respectively.

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