Rendiconti del Seminario Matematico della Università di Padova


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Volume 133, 2015, pp. 173–195
DOI: 10.4171/RSMUP/133-9

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

S. Kiani[1], H.R. Maimani[2], M.R. Pournaki[3] and S. Yassemi[4]

(1) Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
(2) School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5746, Tehran, Iran
(3) School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
(4) School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

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.

Keywords: Unit graph, domination number, total domination number, finite ring

Kiani S., Maimani H.R., Pournaki M.R., Yassemi S.: Classification of rings with unit graphs having domination number less than four. Rend. Sem. Mat. Univ. Padova 133 (2015), 173-195. doi: 10.4171/RSMUP/133-9