On the domination and signed domination numbers of zero-divisor graph
| Main Authors: | Vatandoost, Ebrahim; Department of Basic Science, Imam Khomeini International University, Qazvin, Iran, Ramezani, Fatemeh; Department of Basic Science, Imam Khomeini International University, Qazvin, Iran |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2016
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/83 http://www.ejgta.org/index.php/ejgta/article/view/83/pdf_21 |
Daftar Isi:
- Let $R$ be a commutative ring (with 1) and let $Z(R)$ be its set of zero-divisors. The zero-divisor graph $\Gamma(R)$ has vertex set $Z^*(R)=Z(R) \setminus \lbrace0 \rbrace$ and for distinct $x,y \in Z^*(R)$, the vertices $x$ and $y$ are adjacent if and only if $xy=0$. In this paper, we consider the domination number and signed domination number on zero-divisor graph $\Gamma(R)$ of commutative ring $R$ such that for every $0 \neq x \in Z^*(R)$, $x^2 \neq 0$. We characterize $\Gamma(R)$ whose $\gamma(\Gamma(R))+\gamma(\overline{\Gamma(R)}) \in \lbrace n+1,n,n-1 \rbrace$, where $|Z^*(R)|=n$.