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