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<p>The Hosoya polynomial captures the distribution of distances between unordered pairs of vertices in a graph and serves as a fundamental tool in chemical graph theory, network analysis, and combinatorics. In this paper, we compute the Hosoya polynomial for the joined union of graphs. As an application, we compute closed form expressions for the Hosoya polynomials of several graph families that arise from this construction. To facilitate reproducibility and further research, we also provide an implementation in <Emphasis FontCategory="NonProportional">SageMath</Emphasis> that computes the Hosoya polynomial for joined union, enabling algorithmic verification and extension of our results.</p>

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On the Hosoya Polynomial of Joined Union Graph: Theory and Code

  • 期刊论文

  • 发表日期：

    2026年1月27日

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  • Yogendra Singh,
  • Aditya Singh,
  • Anand Kumar Tiwari

摘要

The Hosoya polynomial captures the distribution of distances between unordered pairs of vertices in a graph and serves as a fundamental tool in chemical graph theory, network analysis, and combinatorics. In this paper, we compute the Hosoya polynomial for the joined union of graphs. As an application, we compute closed form expressions for the Hosoya polynomials of several graph families that arise from this construction. To facilitate reproducibility and further research, we also provide an implementation in SageMath that computes the Hosoya polynomial for joined union, enabling algorithmic verification and extension of our results.