The embedding of line graphs associated to the zero-divisor graphs of commutative rings |
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Authors: | Hung-Jen Chiang-Hsieh Pei-Feng Lee Hsin-Ju Wang |
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Institution: | 1.Department of Mathematics,National Chung Cheng University,Chiayi,Taiwan |
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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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