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Paper Information

Journal:   MATHEMATICAL SCIENCES   2018 , Volume 12 , Number 1; Page(s) 1 To 6.
 
Paper: 

The annihilating graph of a ring

 
 
Author(s):  SHAFIEi Z., MAGHASEDI M.*, HEYDARI F., Khojasteh S.
 
* Department of Mathematics, Karaj Azad University, Karaj, Iran
 
Abstract: 
Let A be a commutative ring with unity. The annihilating graph of A, denoted by Gð AÞ , is a graph whose vertices are all non-trivial ideals of A and two distinct vertices I and J are adjacent if and only if Annð IÞ Annð JÞ ¼ 0. For every commutative ring A, we study the diameter and the girth of Gð AÞ . Also, we prove that if Gð AÞ is a triangle-free graph, then Gð AÞ is a bipartite graph. Among other results, we show that if Gð AÞ is a tree, then Gð AÞ is a star or a double star graph. Moreover, we prove that the annihilating graph of a commutative ring cannot be a cycle. Let n be a positive integer number. We classify all integer numbers n for which Gð ZnÞ is a complete or a planar graph. Finally, we compute the domination number of Gð ZnÞ .
 
Keyword(s): Annihilating graph ,Diameter ,Girth ,Planarity
 
 
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APA: Copy

SHAFIEI, Z., & MAGHASEDI, M., & HEYDARI, F., & KHOJASTEH, S. (2018). The annihilating graph of a ring. MATHEMATICAL SCIENCES, 12(1), 1-6. https://www.sid.ir/en/journal/ViewPaper.aspx?id=668541



Vancouver: Copy

SHAFIEI Z., MAGHASEDI M., HEYDARI F., KHOJASTEH S.. The annihilating graph of a ring. MATHEMATICAL SCIENCES. 2018 [cited 2021November28];12(1):1-6. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=668541



IEEE: Copy

SHAFIEI, Z., MAGHASEDI, M., HEYDARI, F., KHOJASTEH, S., 2018. The annihilating graph of a ring. MATHEMATICAL SCIENCES, [online] 12(1), pp.1-6. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=668541.



 
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