Nearly Gorenstein rings arising from finite graphs

TL;DR

This paper classifies certain algebraic structures called nearly Gorenstein rings that arise from specific classes of finite graphs, expanding understanding of their algebraic and combinatorial properties.

Contribution

It provides a complete classification of nearly Gorenstein rings associated with complete multipartite and perfect graphs.

Findings

Classified nearly Gorenstein edge rings of complete multipartite graphs.

Classified nearly Gorenstein stable set rings of finite perfect graphs.

Enhanced understanding of the relationship between graph properties and algebraic structures.

Abstract

The classification of complete multipartite graphs whose edge rings are nearly Gorenstein as well as that of finite perfect graphs whose stable set rings are nearly Gorenstein is achieved.