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Symmetric graph of a ring with involution

Author

Listed:
  • W. M. Fakeih

    (King Abdulaziz University)

  • T. Asir

    (Madurai Kamaraj University)

Abstract

Let R be a ring with involution $$*$$ ∗ . The graph $$S\varGamma ^*(R)$$ S Γ ∗ ( R ) is obtained by letting all the elements of nonzero zero-divisors of R to be the vertices and defining distinct vertices x and y to be adjacent if $$xy=0$$ x y = 0 (or $$yx=0$$ y x = 0 ) and $$yx^*=0$$ y x ∗ = 0 . The graph $$S\varGamma ^*(R)$$ S Γ ∗ ( R ) is a generalization of the well known zero-divisor graph of R. In this paper, some graph theoretical properties of the $$*-$$ ∗ - symmetric graph are studied.

Suggested Citation

  • W. M. Fakeih & T. Asir, 2023. "Symmetric graph of a ring with involution," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(1), pages 288-296, March.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:1:d:10.1007_s13226-022-00253-6
    DOI: 10.1007/s13226-022-00253-6
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