International journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN:2313-626X

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 Volume 6, Issue 8 (August 2019), Pages: 71-76

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 Original Research Paper

 Title: M-polynomial and entropy of para-line graph of naphthalene

 Author(s): Tanweer Ul Islam 1, Zeeshan Saleem Mufti 2, *, Hifza Iqbal 2, Samreen Miraj 2, Madiha Ajmal 2

 Affiliation(s):

 1Department of Economics, National University of Sciences and Technology, Islamabad, Pakistan
 2Department of Mathematics and Statistics, The University of Lahore, Lahore Campus, Lahore, Pakistan

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-6765-6595

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2019.08.010

 Abstract:

The objective of this paper is to explore the stability of naphthalene (m, n). For a single unit of naphthalene, its stability is less relative to self-dimerization. For two units of naphthalene, there is a slight increase in stability and self-dimerization decreases as well. However, for (m, n) unit of Naphthalene, its stability increases rapidly and self-dimerization decreases proportionately. The M-Polynomial is extracted from praline graph of naphthalene which further yielded several degree-based topological indices. The analytical information function of a graph is entropy which uses probability density on the set of vertices. This paper computes the entropy of para-line graph of naphthalene (m, n) and its relationship with Randic index. 

 © 2019 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: M-polynomial, Graph entropy, Para-line graph of naphthalene

 Article History: Received 25 January 2019, Received in revised form 11 June 2019, Accepted 13 June 2019

 Acknowledgement:

No Acknowledgement.

 Compliance with ethical standards

 Conflict of interest:  The authors declare that they have no conflict of interest.

 Citation:

 Ul Islam T, Mufti ZS, and Iqbal H et al. (2019). M-polynomial and entropy of para-line graph of naphthalene. International Journal of Advanced and Applied Sciences, 6(8): 71-76

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 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 

 Tables

 Table 1 Table 2

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