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<p>The Harary Index is an important topological parameter for examining the structure of a graph. This work presents a quantitative analysis of the structural features of zero-divisor graph using the Harary Index. In this research article, we compute the Harary Index for the zero-divisor graph of the ring of upper triangular matrices over a finite commutative ring and non commutative ring. In this study, we have computed the Harary index for directed and undirected zero-divisor graph obtained from upper triangular matrix <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((M_3)\)</EquationSource> </InlineEquation>.</p>

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Harary index of the zero divisor graph of upper triangular matrices

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月4日

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  • Omaima Alshanqiti,
  • Sahil Sharma,
  • Vijay Kumar Bhat

摘要

The Harary Index is an important topological parameter for examining the structure of a graph. This work presents a quantitative analysis of the structural features of zero-divisor graph using the Harary Index. In this research article, we compute the Harary Index for the zero-divisor graph of the ring of upper triangular matrices over a finite commutative ring and non commutative ring. In this study, we have computed the Harary index for directed and undirected zero-divisor graph obtained from upper triangular matrix \((M_3)\) .