Volume 16, Issue 1 (4-2021)                   IJMSI 2021, 16(1): 97-104 | Back to browse issues page

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Kourehpaz A, Nikandish R. On Eulerianity and Hamiltonicity in Annihilating-ideal Graphs. IJMSI. 2021; 16 (1) :97-104
URL: http://ijmsi.ir/article-1-1251-en.html
Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either Eulerian or Hamiltonian are given.
Type of Study: Research paper | Subject: General

1. G. Aalipour, S. Akbari, R. Nikandish, M. J. Nikmehr, F. Shaveisi, On the coloring of the annihilating-ideal graph of a commutative ring, Discrete Math. 312 (2012) 2620--2626. [DOI:10.1016/j.disc.2011.10.020]
2. S. Akbari, A. Alilou, J. Amjadi, S. M. Sheikholeslami, The Co-annihilating-ideal graphs of commutative rings, Canad. Math. Bull. 60(2017), 3--11. [DOI:10.4153/CMB-2016-017-1]
3. D. F. Anderson, A. Badawi, On the total graph of a commutative ring without the zero element, J. Algebra Appl. 11, 1250074 (2012) [18 pages]. [DOI:10.1142/S0219498812500740]
4. M. F. Atiyah, I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Company (1969).
5. A. Badawi, On the dot product graph of a commutative ring, Comm. Algebra 43 (2015) 43--50. [DOI:10.1080/00927872.2014.897188]
6. M. Behboodi and Z. Rakeei, The annihilating-ideal graph of commutative rings I, J. Algebra Appl. 10 (2011) 727--739. [DOI:10.1142/S0219498811004896]
7. R. Nikandish, H. R. Maimani, H. Izanloo, The annihilating-ideal graph of $mathbb{Z}_{n}$ is weakly perfect, Contribituins to Discrete Mathematics 11 (2016) 16--21.
8. F. Shaveisi, The central vertices and radius of the regular graph of ideals, Transactions on Combinatorics (TOC) 6 (2017) 1--13.
9. D. B. West, Introduction to Graph Theory, 2nd ed., Prentice Hall, Upper Saddle River (2001).
10. H. Y. Yu, T. Wu, Commutative rings $R$ whose $C(mathbb{AG}(R))$ consists only of triangles, Comm. Algebra 43 (2015) 1076--1097. [DOI:10.1080/00927872.2013.847950]

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