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Computing Certain Topological Indices of Generalised Mycielskian Graphs

Received: 10 February 2017    Accepted: 24 March 2017    Published: 14 April 2017
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Abstract

The generalized Mycielskians are the generalization of the Mycielski graphs, which were introduced by Mycielski in 1955. A topological index is a numeric parameter mathematically derived from a graph and is invariant under automorphism of graphs. Topological indices are widely used for establishing correlations between the structure of a molecular compound and its different physico-chemical properties. This paper investigates different degree-based topological indices of the generalized Mycielskians of G.

Published in International Journal of Discrete Mathematics (Volume 2, Issue 3)
DOI 10.11648/j.dmath.20170203.19
Page(s) 112-118
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), 2024. Published by Science Publishing Group

Keywords

Topological Index, Degree of a Vertex, Generalized Mycielskian Graphs, Graph Operations

References
[1] I. Gutman, N. Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535-538.
[2] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (4) (2015) 1184-1190.
[3] N. De, S. M. A. Nayeem and A. Pal, F-index of some graph operations, Discret. Math. Algorithms Appl. (2016), doi: 10.1142/S1793830916500257.
[4] N. De, S. M. A. Nayeem and A. Pal, The F-coindex of some graph operations, SpringerPlus 5: 221 (2016), doi: 10.1186/s40064-016-1864-7.
[5] N. De, S. M. A. Nayeem, Computing the F-index of nanostar dendrimers, Pacific Science Review A: Natural Science and Engineering, doi: 10.1016/j.psra.2016.06.001.
[6] N. De, F-index of total transformation graphs, arXiv: 1606.05989.
[7] H. Abdo, D. Dimitrov and I. Gutman, On extremal trees with respect to the F-index, arXiv: 1509.03574v2.
[8] N. De, F-index of bridge and chain graphs, Mal. J. Fund. Appl. Sci., 12 (4), 2016, 109-113.
[9] A. Miličević, S. Nikolić, and N. Trinajstić, On reformulated Zagreb indices, Mol. Divers., 8 (4), 2004, 393–399.
[10] B. Zhou, N. Trinajstić, Some properties of the reformulated Zagreb indices, J. Math. Chem., 48 (3), 2010, 714–719.
[11] A. Ilić, B. Zhou, On reformulated Zagreb indices, Discret. Appl. Math., 160 (3), 2012, 204–209.
[12] G. Su, L. Xiong, L. Xu, and B. Ma, On the maximum and minimum first reformulated Zagreb index of graphs with connectivity at most k, Filomat, 25 (4), 2011, 75–83.
[13] N. De, Some bounds of reformulated Zagreb indices, Appl. Math. Sci., 6 (101), 2012, 5005–5012.
[14] N. De, Reformulated Zagreb indices of dendrimers, Math. Aeterna, 3 (2), 2013, 133-138.
[15] N. De, S. M. A. Nayeem, and A. Pal, Reformulated first Zagreb index of some graph operations, Mathematics 3 (4), 2015, 945-960.
[16] G. H. Shirdel, H. Rezapour and A. M. Sayadi, The hyper-Zagreb index of graph operations, Iran. J. Math. Chem., 4 (2), 2013, 213-220.
[17] M. Veylaki, M. J. Nikmehr and H. A. Tavallaee, The third and hyper-Zagreb coindices of some graph operations, J. Appl. Math. Comput., 50 (1-2), 2016, 315–325.
[18] B. Basavanagoud, S. Patil, A note on Hyper-Zagreb index of graph operations, Iran. J. Math. Chem., 7 (1), 2016, 89-92.
[19] M. R. Farahani, Computing the hyper-Zagreb index of hexagonal nanotubes, J. Chem. Mate. Res., 2 (1), 2015, 16-18.
[20] W. Gao, W. Wang and M. R. Farahani, Topological Indices Study of Molecular Structure in Anticancer Drugs, J. Chem. (2016), http://dx.doi.org/10.1155/2016/3216327.
[21] J. Mycielski, Sur le coloriage des graphes, Colloq. Math., 3, 1955, 161–162.
[22] M. Caramia, P. Dell Olmo, A lower bound on the chromatic number of Mycielski graphs, Discrete Math., 235 (1-2), 2001, 79–86.
[23] V. Chvatal, The minimality of the Mycielski graph, Lecture Notes in Math., 406, 1974, 243–246.
[24] K. L. Collins, K. Tysdal, Dependent edges in Mycielski graphs and 4-colorings of 4- skeletons, J. Graph Theory, 46 (4), 2004, 285–296.
[25] A. Jerline, Dhanalakshmi K and B. Michaelraj L, The first and the second Zagreb indices of the generalized Mycielskian of graphs, Elect. Notes Discrete Math., 53, 2016, 239–258.
[26] M. O. Albertson, The Irregularity of a graph, Ars Comb., 46, 1997, 219--225.
[27] H. Abdo, D. Dimitrov, The irregularity of graphs under graph operations, Discuss. Math. Graph Theory, 34 (2), 2014, 263--278.
[28] F. K. Bell, A note on the irregularity of graphs, Linear Algebra Appl., 161, 1992, 45--54.
[29] M. Tavakoli, F. Rahbarnia and A. R. Ashrafi, Some new results on irregularity of graphs, J. Appl. Math. Informatics, 32, 2014, 675--685.
[30] N. De, A. Pal and S. M. A. Nayeem, The irregularity of some composite graphs, Int. J. Appl. Comput. Math., 2 (3), 2016, 411–420, DOI 10.1007/s40819-015-0069-z.
[31] W. Luo, B. Zhou, On the irregularity of trees and unicyclic graphs with given matching number, Util. Math., 83, (2010), 141-147.
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    Nilanjan De. (2017). Computing Certain Topological Indices of Generalised Mycielskian Graphs. International Journal of Discrete Mathematics, 2(3), 112-118. https://doi.org/10.11648/j.dmath.20170203.19

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    ACS Style

    Nilanjan De. Computing Certain Topological Indices of Generalised Mycielskian Graphs. Int. J. Discrete Math. 2017, 2(3), 112-118. doi: 10.11648/j.dmath.20170203.19

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    AMA Style

    Nilanjan De. Computing Certain Topological Indices of Generalised Mycielskian Graphs. Int J Discrete Math. 2017;2(3):112-118. doi: 10.11648/j.dmath.20170203.19

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  • @article{10.11648/j.dmath.20170203.19,
      author = {Nilanjan De},
      title = {Computing Certain Topological Indices of Generalised Mycielskian Graphs},
      journal = {International Journal of Discrete Mathematics},
      volume = {2},
      number = {3},
      pages = {112-118},
      doi = {10.11648/j.dmath.20170203.19},
      url = {https://doi.org/10.11648/j.dmath.20170203.19},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170203.19},
      abstract = {The generalized Mycielskians are the generalization of the Mycielski graphs, which were introduced by Mycielski in 1955. A topological index is a numeric parameter mathematically derived from a graph and is invariant under automorphism of graphs. Topological indices are widely used for establishing correlations between the structure of a molecular compound and its different physico-chemical properties. This paper investigates different degree-based topological indices of the generalized Mycielskians of G.},
     year = {2017}
    }
    

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    T1  - Computing Certain Topological Indices of Generalised Mycielskian Graphs
    AU  - Nilanjan De
    Y1  - 2017/04/14
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    N1  - https://doi.org/10.11648/j.dmath.20170203.19
    DO  - 10.11648/j.dmath.20170203.19
    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
    SP  - 112
    EP  - 118
    PB  - Science Publishing Group
    SN  - 2578-9252
    UR  - https://doi.org/10.11648/j.dmath.20170203.19
    AB  - The generalized Mycielskians are the generalization of the Mycielski graphs, which were introduced by Mycielski in 1955. A topological index is a numeric parameter mathematically derived from a graph and is invariant under automorphism of graphs. Topological indices are widely used for establishing correlations between the structure of a molecular compound and its different physico-chemical properties. This paper investigates different degree-based topological indices of the generalized Mycielskians of G.
    VL  - 2
    IS  - 3
    ER  - 

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Author Information
  • Department of Basic Sciences and Humanities, Calcutta Institute of Engineering and Management, Kolkata, West Bengal, India

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