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Cohen–macaulayness of a class of graphs versus the class of their complements

Ashitha, T ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2021.112525
  3. Publisher: Elsevier B.V , 2021
  4. Abstract:
  5. Let n≥2 be an integer. The graph G(n) is obtained by letting all the elements of {0,…,n−1} to be the vertices and defining distinct vertices x and y to be adjacent if and only if gcd⁡(x+y,n)=1. In this paper, well-coveredness, Cohen–Macaulayness, vertex-decomposability and Gorensteinness of these graphs and their complements are characterized. These characterizations provide large classes of Cohen–Macaulay and non Cohen–Macaulay graphs. © 2021 Elsevier B.V
  6. Keywords:
  7. Well-covered graph ; Cohen–Macaulay graph ; Vertex-decomposable graph ; Gorenstein graph
  8. Source: Discrete Mathematics ; Volume 344, Issue 10 , 2021 ; 0012365X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0012365X21002387