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<p>In&#xa0;this paper, we study structural properties of comaximal ideal graphs and their complements, focusing on well-coveredness, well-dominatedness, and Cohen–Macaulayness.A&#xa0;graph is well-covered if all its maximal independent sets have the same cardinality, and well-dominated if all its minimal dominating sets have the same cardinality.These properties are useful for describing uniformity phenomena in graph structures.The&#xa0;Cohen–Macaulay property gives an&#xa0;additional algebraic perspective by relating combinatorial features of graphs to commutative algebra.We&#xa0;characterize finite commutative rings with unity whose comaximal ideal graphs and complements have these properties and thereby describe how the corresponding algebraic structure is reflected in graph-theoretic invariants.</p>

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Well-Coveredness and Cohen–Macaulayness of Comaximal Ideal Graphs

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • M. Sivankutty

摘要

In this paper, we study structural properties of comaximal ideal graphs and their complements, focusing on well-coveredness, well-dominatedness, and Cohen–Macaulayness.A graph is well-covered if all its maximal independent sets have the same cardinality, and well-dominated if all its minimal dominating sets have the same cardinality.These properties are useful for describing uniformity phenomena in graph structures.The Cohen–Macaulay property gives an additional algebraic perspective by relating combinatorial features of graphs to commutative algebra.We characterize finite commutative rings with unity whose comaximal ideal graphs and complements have these properties and thereby describe how the corresponding algebraic structure is reflected in graph-theoretic invariants.