On the annihilator graph of a commutative ring

Z. Barati, M. Afkhami, G. Kalaimurugan and P. Vignesh
Additional contact information
Z. Barati: Kosar University of Bojnord
M. Afkhami: University of Neyshabur
G. Kalaimurugan: Thiruvalluvar University
P. Vignesh: Thiruvalluvar University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 4, 923-931

Abstract: Abstract Let R be a commutative ring with nonzero identity and $$Z^*(R)$$ Z ∗ ( R ) be the set of all non-zero zero-divisors of R. The annihilator graph AG(R) is a simple graph with vertex set $$Z^*(R)$$ Z ∗ ( R ) and two distinct vertices x and y are adjacent if and only if $$\text{ ann }(xy)\ne \text{ ann }(x) \cup \text{ ann }(y)$$ ann ( x y ) ≠ ann ( x ) ∪ ann ( y ) . In this paper, we study the embedding of the iterated line graphs of AG(R) in a plane. We characterize all finite commutative rings with respect to their planar indices, ring indices, outerplanar indices and generalized outerplanar indices.

Keywords: Annihilator graph; Line graph; Iterated line graph; Planar index; Outerplanar index; Ring index; 05C10; 05C25; 13A15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00198-2

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