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A class of graphs with a few well-covered members

Ashitha, T ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1016/j.exmath.2021.03.001
  3. Publisher: Elsevier GmbH , 2021
  4. Abstract:
  5. For a given finite commutative ring R with 1≠0, one may associate a graph which is called the total graph of R and it is denoted by T(R). This graph has R as the vertex set and its two distinct vertices x and y are adjacent exactly whenever x+y is a zero-divisor of R. In this note, we prove that T(R) is well-covered if and only if either R is local or 2 is a zero-divisor. © 2021 Elsevier GmbH
  6. Keywords:
  7. Finite ring ; Total graph ; Maximal independent set ; Well-covered graph
  8. Source: Expositiones Mathematicae ; Volume 39, Issue 2 , 2021 , Pages 302-308 ; 07230869 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0723086921000165