The PI(Padmakar-Ivan) Index of Polyominoes

P. Gayathri; K. R. Subramanian

doi:doi:10.11648/j.dmath.20160101.11

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The PI(Padmakar-Ivan) Index of Polyominoes

P. Gayathri, K. R. Subramanian

Published in International Journal of Discrete Mathematics (Volume 1, Issue 1)

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.

Published in	International Journal of Discrete Mathematics (Volume 1, Issue 1)
DOI	10.11648/j.dmath.20160101.11
Page(s)	1-4
Creative Commons	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.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

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

References

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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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ACS 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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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - The PI(Padmakar-Ivan) Index of Polyominoes
AU  - P. Gayathri
AU  - K. R. Subramanian
Y1  - 2016/12/26
PY  - 2016
N1  - https://doi.org/10.11648/j.dmath.20160101.11
DO  - 10.11648/j.dmath.20160101.11
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
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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.
VL  - 1
IS  - 1
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Author Information

P. Gayathri

Department of Mathematics, A. V. College (Autonomous), Mayiladuthurai, Tamilnadu, India
K. R. Subramanian

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

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APA Style

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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ACS 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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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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - The PI(Padmakar-Ivan) Index of Polyominoes
AU  - P. Gayathri
AU  - K. R. Subramanian
Y1  - 2016/12/26
PY  - 2016
N1  - https://doi.org/10.11648/j.dmath.20160101.11
DO  - 10.11648/j.dmath.20160101.11
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 1
EP  - 4
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20160101.11
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.
VL  - 1
IS  - 1
ER  -

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