Classification of rings with unit graphs having domination number less than four

  • S. Kiani

    Islamic Azad University, Tehran, Iran
  • H.R. Maimani

    Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
  • M.R. Pournaki

    Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
  • S. Yassemi

    Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

Abstract

Let be a finite commutative ring with nonzero identity. The unit graph of is the graph obtained by setting all the elements of to be the vertices and defining distinct vertices and to be adjacent if and only if is a unit element of . In this paper, a classification of finite commutative rings with nonzero identity in which their unit graphs have domination number less than four is given.

Cite this article

S. Kiani, H.R. Maimani, M.R. Pournaki, S. Yassemi, Classification of rings with unit graphs having domination number less than four. Rend. Sem. Mat. Univ. Padova 133 (2015), pp. 173–195

DOI 10.4171/RSMUP/133-9