Rendiconti del Seminario Matematico della Università di Padova


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

Published online: 2015-06-01

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) Islamic Azad University, Tehran, Iran
(2) Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
(3) Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
(4) Institute for Research in Fundamental Sciences (IPM), 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