On the domination and signed domination numbers of zero-divisor graph

Ebrahim Vatandoost, Fatemeh Ramezani


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 $|Z^*(R)|=n$.


domination number, signed domination number, zero-divisor graph

Full Text:


DOI: http://dx.doi.org/10.5614/ejgta.2016.4.2.3


  • There are currently no refbacks.

ISSN: 2338-2287

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View EJGTA Stats