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European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
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133
2015
0
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
Unit graph, domination number, total domination number, finite ring
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.
Combinatorics
Commutative rings and algebras
173
195
10.4171/RSMUP/133-9
http://www.ems-ph.org/doi/10.4171/RSMUP/133-9