Metric dimension of the complement of the zero-divisor graph

• R. Nikandish ^[1] ; M. Jalali ^[2]
  1. [1] University of Technology

     University of Technology

     Rusia

     
  2. [2] Islamic Azad University

     Islamic Azad University

     Irán

     
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 118, Nº. 4, 2024, 1 págs.
• Idioma: inglés
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• Resumen

  • Let S be the smallest subset of vertices in a graph G such that every vertex outside of S has a unique distance vector with respect to S. Then |S| is defined as the metric dimension of G and it is denoted by . In this paper, the metric dimension of the complement of the zero-divisor graph associated with a commutative ring is discussed. Several formulae for different classes of rings are given