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Some new version of resistance distance-based topological indices of complete bipartite networks

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Abstract

Bipartite networks, also known as two-mode networks, are those in which nodes are separated into two disjoint sets and edges only connect nodes in different sets. These networks have numerous applications across different domains. For instance, in particle physics, bipartite networks are used to represent particle interactions and the detectors that observe them. Each set of nodes can represent a variety of particles and detectors, while edges indicate interactions or detections. These networks aid in understanding particle interactions, tracking particles, and optimizing detector design. An electrical network may be viewed as a graph with nodes and links. If the edges are replaced by resistors of resistance 1 (ohm), then resistance distance between two nodes within a connected network is characterized as the overall effective resistance linking them. This work derives some new version of resistance-based indices (\({\mathcal{R}}{\text{-indices}}\)) of a complete bipartite network. These recently introduced indices are helpful in the analysis of electrical networks.

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Acknowledgements

The authors are grateful to Prof. Ali Ahmad from Jazan University for his fruitful suggestions.

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No funding is available for this study.

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Authors and Affiliations

  1. Department of Mathematics, University of Sialkot, Sialkot, 51310, Pakistan

    Shahid Zaman & Ahmed Raza

  2. Department of Mathematical Sciences, Karakoram International University Gilgit, Gilgit, 15100, Pakistan

    Asad Ullah

Authors
  1. Shahid Zaman
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  2. Ahmed Raza
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  3. Asad Ullah
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All authors have equally contributed to this manuscript in all stages, from conceptualization to the write up of final draft.

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Correspondence to Shahid Zaman.

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Zaman, S., Raza, A. & Ullah, A. Some new version of resistance distance-based topological indices of complete bipartite networks. Eur. Phys. J. Plus 139, 357 (2024). https://doi.org/10.1140/epjp/s13360-024-05127-w

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