31 خرداد 1403
سعيد باقري (بازنشسته)

سعید باقری (بازنشسته)

مرتبه علمی: استادیار
نشانی: ملایر-کیلومتر 4 جاده اراک-دانشگاه ملایر- دانشکده علوم ریاضی- گروه ریاضی
تحصیلات: دکترای تخصصی / ریاضی جبر
تلفن:
دانشکده: دانشکده علوم ریاضی و آمار

مشخصات پژوهش

عنوان
The Annihilator Graph of a 0-Distributive Lattice
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
Distributive lattice, Annihilator graph, Zero-divisor graph.
سال
2018
مجله transactions on combinatorics
پژوهشگران سعید باقری (بازنشسته)

چکیده

In this article, for a lattice L, we define and investigate the annihilator graph ag(L) of L which contains the zero-divisor graph of L as a subgraph. Also, for a 0-distributive lattice 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 L with non zero Z(L), we show that the annihilator graph ag(L) is the same as the zero-divisor graphof L if and only if L has exactly two minimal prime ideals. Among other things, we consider the annihilator graph ag(L) of the lattice L = (D(n); |) containing all positive divisors of a non-prime natural number 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 the annihilator graph ag(D(n)) and the zero-divisor graph of D(n) are planar, Eulerian or Hamiltonian.