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Dergiler / International Electronic Journal of Algebra / 2023 / Cilt: 33 - Sayı: 33

Planar index and outerplanar index of zero-divisor graphs of commutative rings without identity

G. KALAIMURUGAN
P. VIGNESH
M. AFKHAMI
Z. BARATI
Sayfa
18–33
Yayın Tarihi
2023-01-09
DOI
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Further, we establish the planar index, ring index and outerplanar index of the zero-divisor graphs of finite commutative rings without identity.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let $R$ be a commutative ring without identity.
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Temel Bulgular & Veri:The zero-divisor graph of $R,$ denoted by $\Gamma(R)$ is a graph with vertex set $Z(R)\setminus \{0\}$ which is the set of all nonzero zero-divisor elements of $R,$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0.$ In this paper, we characterize the rings whose zero-divisor graphs are ring graphs and outerplanar graphs.
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Sonuç & Katkı:Further, we establish the planar index, ring index and outerplanar index of the zero-divisor graphs of finite commutative rings without identity.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Zero-divisor graph · line graph · iterated line graph

Abstract

Let $R$ be a commutative ring without identity. The zero-divisor graph of $R,$ denoted by $\Gamma(R)$ is a graph with vertex set $Z(R)\setminus \{0\}$ which is the set of all nonzero zero-divisor elements of $R,$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy=0.$ In this paper, we characterize the rings whose zero-divisor graphs are ring graphs and outerplanar graphs. Further, we establish the planar index, ring index and outerplanar index of the zero-divisor graphs of finite commutative rings without identity.

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Bu Makaleye Atıf Yap

KALAIMURUGAN, G., VIGNESH, P., AFKHAMI, M., BARATI, Z. (2023). Planar index and outerplanar index of zero-divisor graphs of commutative rings without identity. International Electronic Journal of Algebra, Cilt: 33 - Sayı: 33, 18–33. https://ajindex.com/articles/876039

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Kaynakça (13)

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