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This is a Quantitative Study study.

September 28, 2025Open Access

Embeddings of the line graphs associated with the essential graphs of commutative rings

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The line graphs of the essential graphs of finite commutative rings can be classified based on their embedding properties.
Results identify which finite commutative rings have their essential graph's line graph as planar, outerplanar, or with specific topology limits.
The research characterizes non-local rings whose zero-divisor graphs' line graphs are outerplanar, enhancing understanding of their structure.
The findings shed light on the relationships between ring properties and surface embeddings within graph theory.

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This study reveals the planar properties of line graphs from essential graphs in commutative rings, suggesting key classifications of surfaces.

Jain et al. (2025) studied this question.

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This study reveals the planar properties of line graphs from essential graphs in commutative rings, suggesting key classifications of surfaces.