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The embedding of line graphs associated to the zero-divisor graphs of commutative rings

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Abstract

Let R be a commutative ring with identity and denote Γ(R) for its zero-divisor graph. In this paper, we study the minimal embedding of the line graph associated to Γ(R), denoted by L(Γ(R)), into compact surfaces (orientable or non-orientable) and completely classify all finite commutative rings R such that the line graphs associated to their zero-divisor graphs have genera or crosscaps up to two.

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Authors and Affiliations

  1. Department of Mathematics, National Chung Cheng University, Chiayi, 621, Taiwan

    Hung-Jen Chiang-Hsieh, Pei-Feng Lee & Hsin-Ju Wang

Authors
  1. Hung-Jen Chiang-Hsieh
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  2. Pei-Feng Lee
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  3. Hsin-Ju Wang
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Correspondence to Hung-Jen Chiang-Hsieh.

Additional information

The work was supported by research grants from National Science Coancilt of Taiwan.

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Chiang-Hsieh, HJ., Lee, PF. & Wang, HJ. The embedding of line graphs associated to the zero-divisor graphs of commutative rings. Isr. J. Math. 180, 193–222 (2010). https://doi.org/10.1007/s11856-010-0101-2

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  • DOI: https://doi.org/10.1007/s11856-010-0101-2

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