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This research explores the intersection of graph theory and chemical graph theory by investigating the connectivity indices in the prime ideal sum graph PIS(R) of a commutative ring R with identity. This graph, comprising non-zero proper ideals as vertices and establishes edges between distinct ideals I and J only if their sum, \(I+J\) , forms a prime ideal in R. Focusing on \(R=\mathbb {Z}_n\) , we calculate the Randi c index and Sum-connectivity index for key cases ( \(n=p^{\beta },p^2q,p^2q^2,pqr,p^3q,p^2qr, pqrs\) ), where p, q, r, s are distinct primes and \(\beta \ge 3\) is a positive integer. These indices act as numerical representations of molecular structures, aiding in property prediction and the design of new drugs.

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Some Graph Invariants of Prime Ideal Sum Graph of Commutative Ring

  • 会议论文

  • 发表日期：

    2025年

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  • Cihat Abdioğlu,
  • Nadeem Ur Rehman,
  • Shabir Ahmad Mir,
  • Mohd Nazim

摘要

This research explores the intersection of graph theory and chemical graph theory by investigating the connectivity indices in the prime ideal sum graph PIS(R) of a commutative ring R with identity. This graph, comprising non-zero proper ideals as vertices and establishes edges between distinct ideals I and J only if their sum, \(I+J\) , forms a prime ideal in R. Focusing on \(R=\mathbb {Z}_n\) , we calculate the Randi c index and Sum-connectivity index for key cases ( \(n=p^{\beta },p^2q,p^2q^2,pqr,p^3q,p^2qr, pqrs\) ), where p, q, r, s are distinct primes and \(\beta \ge 3\) is a positive integer. These indices act as numerical representations of molecular structures, aiding in property prediction and the design of new drugs.