Turkish Journal of Mathematics
DOI
10.3906/mat-1508-38
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
First Page
824
Last Page
831
Recommended Citation
TOKER, KEMAL
(2016)
"On the zero-divisor graphs of finite free semilattices,"
Turkish Journal of Mathematics: Vol. 40:
No.
4, Article 11.
https://doi.org/10.3906/mat-1508-38
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss4/11
