International Journal of Discrete Mathematics

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The PI(Padmakar-Ivan) Index of Polyominoes

Received: 19 September 2016    Accepted: 18 November 2016    Published: 26 December 2016
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Abstract

The Padmakar – Ivan (PI) index of polyominoes is examined.Efficient calculations of formulas for PI index for the polyominoes are put forward. In chemical graph theory, the PI index is a topological indexof a graph G is defined as , where for edge e = xy, n1 (e) is the number of edges of G lying closer to x than y, n2 (e) is the number of edges of G lying closer to y than x and summation goes over all edges of G. The edges equidistant from x and y are not considered for the calculation of PI index. In this paper, we calculated the PI index of polyominoes like square Polyomino, L-Polyomino,T-Polyomino, Straight-Polyomino and Skew-Polyomino.

DOI 10.11648/j.dmath.20160101.11
Published in International Journal of Discrete Mathematics (Volume 1, Issue 1, December 2016)
Page(s) 1-4
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

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Copyright © The Author(s), 2024. Published by Science Publishing Group

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Keywords

Molecular Graph, Polyominoes, Topological Indices, PI (Padmakar-Ivan)Index

References
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Author Information
  • Department of Mathematics, A. V. College (Autonomous), Mayiladuthurai, Tamilnadu, India

  • Department of Computer Applications, Shrimati Indira Gandhi College, Trichy, Tamilnadu, India

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    P. Gayathri, K. R. Subramanian. (2016). The PI(Padmakar-Ivan) Index of Polyominoes. International Journal of Discrete Mathematics, 1(1), 1-4. https://doi.org/10.11648/j.dmath.20160101.11

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    P. Gayathri; K. R. Subramanian. The PI(Padmakar-Ivan) Index of Polyominoes. Int. J. Discrete Math. 2016, 1(1), 1-4. doi: 10.11648/j.dmath.20160101.11

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    AMA Style

    P. Gayathri, K. R. Subramanian. The PI(Padmakar-Ivan) Index of Polyominoes. Int J Discrete Math. 2016;1(1):1-4. doi: 10.11648/j.dmath.20160101.11

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  • @article{10.11648/j.dmath.20160101.11,
      author = {P. Gayathri and K. R. Subramanian},
      title = {The PI(Padmakar-Ivan) Index of Polyominoes},
      journal = {International Journal of Discrete Mathematics},
      volume = {1},
      number = {1},
      pages = {1-4},
      doi = {10.11648/j.dmath.20160101.11},
      url = {https://doi.org/10.11648/j.dmath.20160101.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.dmath.20160101.11},
      abstract = {The Padmakar – Ivan (PI) index of polyominoes is examined.Efficient calculations of formulas for PI index for the polyominoes are put forward. In chemical graph theory, the PI index is a topological indexof a graph G is defined as , where for edge e = xy, n1 (e) is the number of edges of G lying closer to x than y, n2 (e) is the number of edges of G lying closer to y than x and summation goes over all edges of G. The edges equidistant from x and y are not considered for the calculation of PI index. In this paper, we calculated the PI index of polyominoes like square Polyomino, L-Polyomino,T-Polyomino, Straight-Polyomino and Skew-Polyomino.},
     year = {2016}
    }
    

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    AB  - The Padmakar – Ivan (PI) index of polyominoes is examined.Efficient calculations of formulas for PI index for the polyominoes are put forward. In chemical graph theory, the PI index is a topological indexof a graph G is defined as , where for edge e = xy, n1 (e) is the number of edges of G lying closer to x than y, n2 (e) is the number of edges of G lying closer to y than x and summation goes over all edges of G. The edges equidistant from x and y are not considered for the calculation of PI index. In this paper, we calculated the PI index of polyominoes like square Polyomino, L-Polyomino,T-Polyomino, Straight-Polyomino and Skew-Polyomino.
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