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Pseudo-Gorenstein$^{*}$ Graphs

Takayuki Hibi, Selvi Kara, Dalena Vien

Abstract

Motivated by pseudo-Gorenstein rings in commutative algebra, introduced by Herzog et al., we define pseudo-Gorenstein$^{*}$ graphs and classify them in several natural graph families using independence polynomials.

Pseudo-Gorenstein$^{*}$ Graphs

Abstract

Motivated by pseudo-Gorenstein rings in commutative algebra, introduced by Herzog et al., we define pseudo-Gorenstein graphs and classify them in several natural graph families using independence polynomials.
Paper Structure (7 sections, 20 theorems, 88 equations)

This paper contains 7 sections, 20 theorems, 88 equations.

Table of Contents

  1. Preliminaries
  2. Pseudo-Gorenstein$^{*}$ Cycles and Paths
  3. Pseudo-Gorenstein$^{*}$ Multipartite Graphs
  4. Pseudo-Gorenstein$^{*}$ Cameron--Walker Graphs
  5. Suspension over vertex covers
  6. Suspensions over maximal independent sets: cycles
  7. Suspensions over maximal independent sets: paths

Key Result

Proposition 1

Let $\alpha=\alpha(G)$. We have $h_{\alpha}(G)=(-1)^{\alpha}P_G(-1)$.

Theorems & Definitions (40)

  • Proposition 1
  • proof
  • Theorem 1.1
  • Corollary 1
  • Corollary 2
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 2.1
  • proof
  • ...and 30 more