- Turkish Journal of Mathematics
- Vol: 40 Issue: 4
- On the zero-divisor graphs of finite free semilattices
On the zero-divisor graphs of finite free semilattices
Authors : Kemal Toker
Pages : 824-831
View : 8 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :Let $SL_{X}$ be the free semilattice on a finite nonempty set $X$. There exists an undirected graph $\Gamma(SL_{X})$ associated with $SL_{X}$ whose vertices are the proper subsets of $X$, except the empty set, and two distinct vertices $A$ and $B$ of $\Gamma(SL_{X})$ are adjacent if and only if $A\cup B=X$. In this paper, the diameter, radius, girth, degree of any vertex, domination number, independence number, clique number, chromatic number, and chromatic index of $\Gamma(SL_{X})$ have been established. Moreover, we have determined when $\Gamma(SL_{X})$ is a perfect graph and when the core of $\Gamma(SL_{X})$ is a Hamiltonian graph.Keywords : Finite free semilattice, zero-divisor graph, clique number, domination number, perfect graph, Hamiltonian graph