JournalsrsmupVol. 133pp. 173–195

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

Abstract

Let RR be a finite commutative ring with nonzero identity. The unit graph of RR is the graph obtained by setting all the elements of RR to be the vertices and defining distinct vertices xx and yy to be adjacent if and only if x+yx+y is a unit element of RR. 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