Domination in Commuting Graph and its Complement
| Autor: | Yasser Golkhandy Pour, Ebrahim Vatandoost |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Finite ring
Mathematics::Commutative Algebra Domination analysis Astrophysics::High Energy Astrophysical Phenomena General Mathematics 010102 general mathematics General Physics and Astronomy Mathematics - Rings and Algebras 010103 numerical & computational mathematics General Chemistry 01 natural sciences Upper and lower bounds Graph Vertex (geometry) Combinatorics Rings and Algebras (math.RA) FOS: Mathematics General Earth and Planetary Sciences 0101 mathematics General Agricultural and Biological Sciences Mathematics |
| Zdroj: | Iranian Journal of Science and Technology, Transactions A: Science. 41:383-391 |
| ISSN: | 2364-1819 1028-6276 |
| DOI: | 10.1007/s40995-016-0028-5 |
| Popis: | For each non-commutative ring R, the commuting graph of R is a graph with vertex set $R\setminus Z(R)$ and two vertices $x$ and $y$ are adjacent if and only if $x\neq y$ and $xy=yx$. In this paper, we consider the domination and signed domination numbers on commuting graph $\Gamma(R)$ for non-commutative ring $R$ with $Z(R)=\{0\}$. For a finite ring $R$, it is shown that $\gamma(\Gamma(R)) + \gamma(\overline{\Gamma}(R))=|R|$ if and only if $R$ is non-commutative ring on 4 elements. Also we determine the domination number of $\Gamma(\prod_{i=1}^{t}R_i)$ and commuting graph of non-commutative ring $R$ of order $p^3$, where $p$ is prime. Moreover we present an upper bound for signed domination number of $\Gamma(\prod_{i=1}^{t}R_i)$. Comment: 9 pages in Iranian Journal of Science and Technology, series A- first online 13 June 2016 |
| Databáze: | OpenAIRE |
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