TY - JOUR
ID - 22285
TI - The annihilator graph of a 0-distributive lattice
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - Bagheri, Saeid
AU - Koohi Kerahroodi, Mahtab
AD - Department of Mathematics, Faculty of Mathematical Sciences, Malayer University, Malayer, Iran
AD - Department of Mathematics, Faculty of Mathematical Sciences, Malayer University, Malayer, Iran.
Y1 - 2018
PY - 2018
VL - 7
IS - 3
SP - 1
EP - 18
KW - Distributive lattice
KW - Annihilator graph
KW - Zero-divisor graph
DO - 10.22108/toc.2017.104919.1507
N2 - In this article, for a lattice $mathcal L$, we define and investigate the annihilator graph $mathfrak {ag} (mathcal L)$ of $mathcal L$ which contains the zero-divisor graph of $mathcal L$ as a subgraph. Also, for a 0-distributive lattice $mathcal L$, we study some properties of this graph such as regularity, connectedness, the diameter, the girth and its domination number. Moreover, for a distributive lattice $mathcal L$ with $Z(mathcal L)neqlbrace 0rbrace$, we show that $mathfrak {ag} (mathcal L) = Gamma(mathcal L)$ if and only if $mathcal L$ has exactly two minimal prime ideals. Among other things, we consider the annihilator graph $mathfrak {ag} (mathcal L)$ of the lattice $mathcal L=(mathcal D(n),|)$ containing all positive divisors of a non-prime natural number $n$ and we compute some invariants such as the domination number, the clique number and the chromatic number of this graph. Also, for this lattice we investigate some special cases in which $mathfrak {ag} (mathcal D(n))$ or $Gamma(mathcal D(n))$ are planar, Eulerian or Hamiltonian.
UR - https://toc.ui.ac.ir/article_22285.html
L1 - https://toc.ui.ac.ir/article_22285_719ab505eba5ec2cd4bf741957e5ce29.pdf
ER -