A note on the zero divisor graph of a lattice
Clicks: 235
ID: 46033
2014
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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| Authors | , T. Tamizh Chelvam;Nithya, S.; |
| Journal | transactions on combinatorics |
| Year | 2014 |
| DOI | DOI not found |
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