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Some indices of picture fuzzy graphs and their applications

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Abstract

The connectivity index (CI), Wiener index (WI), and Randic index (RI) play a significant role in modeling various problems such as networking, transportation, and precise location detection. In this research, we explore these three indices within the framework of picture fuzzy graphs (PFGs). Initially, we present the definitions of connectivity index (CI) and Average Connectivity index (ACI) for picture fuzzy graphs. The connectivity index (CI) of a picture fuzzy graph proves to be particularly effective in addressing real-world problems related to precise location detection. As an illustration, in Sect. 4.1, we utilize the connectivity index (CI) of a picture fuzzy graph to identify the most suitable location for a school. Subsequently, we introduce the concepts of Wiener index (WI), Average Wiener index (AWI), and Hyper-Wiener index (WWI) for picture fuzzy graphs (PFGs). In Sect. 4.2, we demonstrate the application of the Wiener index in modeling intra-city journeys. Additionally, we discuss the important characteristics of these topological indices for picture fuzzy graphs. Furthermore, we investigate the relationship between the Randic index (RI) of a picture fuzzy graph and the Randic index of its subgraph, noting that the former is always greater than or equal to the latter.

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Author notes

  1. Waheed Ahmad Khan, Asghar Khan and Hossein Rashmanlou contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, Pakistan

    Waqar Arif & Asghar Khan

  2. Division of science and technology, Department of Mathematics, University of Education Lahore, Attock Campus, Lahore, Punjab, Pakistan

    Waheed Ahmad Khan

  3. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    Hossein Rashmanlou

  4. School of Physics, Damghan University, Damghan, Iran

    Hossein Rashmanlou

Authors
  1. Waqar Arif
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  2. Waheed Ahmad Khan
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  3. Asghar Khan
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  4. Hossein Rashmanlou
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Correspondence to Waqar Arif.

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Arif, W., Khan, W.A., Khan, A. et al. Some indices of picture fuzzy graphs and their applications. Comp. Appl. Math. 42, 253 (2023). https://doi.org/10.1007/s40314-023-02393-9

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  • DOI: https://doi.org/10.1007/s40314-023-02393-9

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