A note on the zero divisor graph of a lattice
Let $L$ be a lattice with the least element $0$. An element $xin L$ is a zero divisor if $xwedge y=0$ for some $yin L^*=Lsetminus left{0right}$. The set of all zero divisors is denoted by $Z(L)$. We associate a simple graph $Gamma(L)$ to $L$ with vertex set $Z(L)^*=Z(L)setminus left{0right}$, the se...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2014-09-01
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| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | http://www.combinatorics.ir/pdf_5626_80f88a878c7d9f2b5f4422c943a90ae7.html |
| Summary: | Let $L$ be a lattice with the least element $0$. An element $xin L$ is a zero divisor if $xwedge y=0$ for some $yin L^*=Lsetminus left{0right}$. The set of all zero divisors is denoted by $Z(L)$. We associate a simple graph $Gamma(L)$ to $L$ with vertex set $Z(L)^*=Z(L)setminus left{0right}$, the set of non-zero zero divisors of $L$ and distinct $x,yin Z(L)^*$ are adjacent if and only if $xwedge y=0$. In this paper, we obtain certain properties and diameter and girth of the zero divisor graph $Gamma(L)$. Also we find a dominating set and the domination number of the zero divisor graph $Gamma(L)$ |
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| ISSN: | 2251-8657 2251-8665 |