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...
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University of Isfahan
2014-09-01
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| Series: | Transactions on Combinatorics |
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| Online Access: | http://www.combinatorics.ir/pdf_5626_80f88a878c7d9f2b5f4422c943a90ae7.html |
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doaj-56af04977b4f4b699332e8810519e8a02020-11-24T21:41:02ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652014-09-01335159A note on the zero divisor graph of a latticeT. Tamizh Chelvam 0 S. Nithya1Manonmaniam Sundaranar UniversityManonmaniam Sundaranar UniversityLet $L$ 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 $Gamma(L)$http://www.combinatorics.ir/pdf_5626_80f88a878c7d9f2b5f4422c943a90ae7.htmlzero divisor graphlatticeatomic latticeidealdominating set |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
T. Tamizh Chelvam S. Nithya |
| spellingShingle |
T. Tamizh Chelvam S. Nithya A note on the zero divisor graph of a lattice Transactions on Combinatorics zero divisor graph lattice atomic lattice ideal dominating set |
| author_facet |
T. Tamizh Chelvam S. Nithya |
| author_sort |
T. Tamizh Chelvam |
| title |
A note on the zero divisor graph of a lattice |
| title_short |
A note on the zero divisor graph of a lattice |
| title_full |
A note on the zero divisor graph of a lattice |
| title_fullStr |
A note on the zero divisor graph of a lattice |
| title_full_unstemmed |
A note on the zero divisor graph of a lattice |
| title_sort |
note on the zero divisor graph of a lattice |
| publisher |
University of Isfahan |
| series |
Transactions on Combinatorics |
| issn |
2251-8657 2251-8665 |
| publishDate |
2014-09-01 |
| description |
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 $Gamma(L)$ |
| topic |
zero divisor graph lattice atomic lattice ideal dominating set |
| url |
http://www.combinatorics.ir/pdf_5626_80f88a878c7d9f2b5f4422c943a90ae7.html |
| work_keys_str_mv |
AT ttamizhchelvam anoteonthezerodivisorgraphofalattice AT snithya anoteonthezerodivisorgraphofalattice AT ttamizhchelvam noteonthezerodivisorgraphofalattice AT snithya noteonthezerodivisorgraphofalattice |
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