Loading...

A large class of graphs with a small subclass of Cohen–Macaulay members

Ashitha, T ; Sharif University of Technology | 2022

25 Viewed
  1. Type of Document: Article
  2. DOI: 10.1080/00927872.2022.2081333
  3. Publisher: Taylor and Francis Ltd , 2022
  4. Abstract:
  5. Let R be a finite commutative ring with nonzero identity. The unit graph of R is the graph in which the vertex set is R, and two distinct vertices x and y are adjacent if and only if x + y is a unit in R. In this paper, we determine when these graphs are well-covered, and then, by applying this result, we characterize the unit graphs whose edge rings are Cohen–Macaulay (Gorenstein). This characterization gives us a large class of non-Cohen–Macaulay graphs. © 2022 Taylor & Francis Group, LLC
  6. Keywords:
  7. Cohen–Macaulay graph ; Finite commutative ring ; Gorenstein graph ; Unit graph ; Well-covered graph
  8. Source: Communications in Algebra ; Volume 50, Issue 12 , 2022 , Pages 5080-5095 ; 00927872 (ISSN)
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/00927872.2022.2081333