Year 2020, Volume 49 , Issue 1, Pages 195 - 207 2020-02-06

Topological properties of face-centred cubic lattice

Muhammad Kamran SİDDİQUİ [1] , Muhammad IMRAN [2] , Muhammad SAEED [3]


Face-centred cubic lattice $FCC(n)$ has attracted large attention in recent years owing to its distinguished properties and non-toxic nature, low-cost, abundance, and simple fabrication process. The graphs of face-centred cubic lattice contain cube points and face centres. A topological index of a chemical graph $G$ is a numeric quantity related to $G$ which describes its topological properties. In this paper, using graph theory tools, we determine the topological indices namely, Randic index, atomic bond connectivity index, Zagreb types indices, Sanskruti index for face-centred cubic lattice $FCC(n)$.
Randic index, atomic bond connectivity index, Zagreb types indices, Sanskruti index, face-centred cubic lattice FCC(n)
  • [1] D. Amic, D. Beslo, B. Lucic, S. Nikolic, N. Trinajstic, The vertex-connectivity index revisited, J. Chem. Inf. Comput. Sci. 38, 819-822, 1998.
  • [2] M. Bača, J. Horváthová, M. Mokrišová, A. Suhányiová, On topological indices of fullerenes, Appl. Math. Comput. 251, 154-161, 2015.
  • [3] R.J. Bie, M. K. Siddiqui, R. Razavi, M. Taherkhani, M. Najaf, Possibility of C38 and Si19Ge19 Nanocages in Anode of Metal Ion Batteries: Computational Examination, Acta Chim. Slov. 65, 303-311, 2018.
  • [4] B. Bollob´as, P. Erdos, Graphs of extremal weights, Ars. Combi. 50, 225-233, 1998.
  • [5] C.R.A. Catlow, Modelling and predicting crystal structures, Interdisciplinary. Sci. Reviews. 40 294-307, 2015.
  • [6] G. Caporossi, I. Gutman, P. Hansen, L. Pavlovic, Graphs with maximum connectivity index, Comput. Bio. Chem. 27, 85-90, 2003.
  • [7] J.H. Conway, N.J.A. Sloane, Sphere packings, lattices, and groups, 2nd ed, Springer- Verlag, New York, 1993.
  • [8] A.A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: Theory and applications, Acta. Appl. Math. 66, 211-249, 2001.
  • [9] T. Doslic, Vertex-weighted Wiener polynomials for composite graphs, Ars. Math.Contemp. 1, 66-80, 2008.
  • [10] E. Estrada, L. Torres, L. Rodr´iguez, I. Gutman, An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes, Indian. J. Chem. 37A, 849-855, 1998.
  • [11] W. Gao and M. K. Siddiqui, Molecular Descriptors of Nanotube, Oxide, Silicate, and Triangulene Networks, J. of. Chem., 2017, 1–10, 2017.
  • [12] W. Gao, M. K. Siddiqui, M. Imran, M. K. Jamil, M.R. Farahani, Forgotten Topological Index of Chemical Structure in Drugs, Saudi Pharm. J. 24, 258-267, 2016.
  • [13] W. Gharibi, A. Ahmad, M. K. Siddiqui, On Zagreb Indices, Zagreb Polynomials of Nanocone and Nanotubes, J. Comput. Theor. Nanosci. 13, 5086-5092, 2016.
  • [14] I. Gutman, C. N. Das, The first Zagreb index 30 years after, MATCH. Commun. Math. Comput. Chem. 50, 83-92, 2004.
  • [15] I. Gutman, K. C. Das, Some Properties of the Second Zagreb Index, MATCH. Commun. Math. Comput. Chem. 50, 103-112, 2004.
  • [16] I. Gutman, B. Furtula , Z. K. Vukicevic, G. Popivoda, On Zagreb indices and Coindices , MATCH. Commun. Math. Comput. Chemmm. 74, 5-16, 2015.
  • [17] I. Gutman, N. Trinajst, Graph theory and molecular orbitals, Total $\pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17, 535-538, 1972.
  • [18] S.M. Hosamani, Computing Sanskruti index of certain nanostructures, J. Appl. Math. Comput. 54, 425–433, 2016.
  • [19] M. Imran, M.K. Siddiqui, M. Naeem, and M.A. Iqbal, On Topological Properties of Symmetric Chemical Structures, Symmetry 10, 1–20, 2018.
  • [20] J.B. Liu, M.K. Siddiqui, M.A. Zahid, M. Naeem, and A.Q. Baig, Topological Properties of Crystallographic Structure of Molecules, Symmetry 10, 1–18, 2018.
  • [21] X. Li, I. Gutman, Mathematical aspects of Randic type molecular structure descriptors, Mathematical chemistry monographs No. 1, Kragujevac, 2006.
  • [22] H. Mujahed, B. Nagy, Exact formula for computing the hyper-Wiener index on rows of unit cells of the face-centred cubic lattice, An. S.t. Univ. Ovidius Constant. 26 (1), 169–187, 2018.
  • [23] M. Randic, On characterization of molecular branching, J. Amer. Chem. Soc. 97 (23), 6609–6615, 1975.
  • [24] Z. Shao, M. K. Siddiqui, and M. H. Muhammad, Computing Zagreb indices and Zagreb polynomials for symmetrical nanotubes, Symmetry. 10(7), 1-16, 2018.
  • [25] M.K. Siddiqui , W. Gharibi, On Zagreb indices, Zagreb polynomials of mesh derived networks, J. Comput. Theor. Nanosci. 13, 8683–8688, 2016.
  • [26] M.K. Siddiqui, M. Imran, and A. Ali, On Zagreb indices, Zagreb polynomials of some nanostar dendrimers, Appl. Math. Comput. 280, 132–139, 2016.
  • [27] M.K. Siddiqui, M. Naeem, N.A. Rahman, and M. Imran, Computing topological indices of certain networks, J. Opto. Adva. Mate. 18 (9-10), 884–892, 2016.
  • [28] D. Vukicevic, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46, 1369–1376, 2009.
  • [29] C. Wang, J. Liu, and S. Wang, Sharp upper bounds for multiplicative Zagreb indices of bipartite graphs with given diameter, Disc. Appl. Math. 227, 156–165, 2017.
  • [30] S. Wang, C. Wang, and J. Liu, On extremal multiplicative Zagreb indices of trees with given domination number, Appl. Math. Comput. 332, 338–350, 2018.
  • [31] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69, 17–20, 1947.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-2607-4847
Author: Muhammad Kamran SİDDİQUİ (Primary Author)
Institution: COMSATS University Islamabad
Country: Pakistan


Orcid: 0000-0002-2827-0462
Author: Muhammad IMRAN
Institution: United Arab Emirates University
Country: United Arab Emirates


Orcid: 0000-0002-3296-5961
Author: Muhammad SAEED
Institution: Riphah International University Islamabad
Country: Pakistan


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms546348, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {195 - 207}, doi = {10.15672/hujms.546348}, title = {Topological properties of face-centred cubic lattice}, key = {cite}, author = {SİDDİQUİ, Muhammad Kamran and IMRAN, Muhammad and SAEED, Muhammad} }
APA SİDDİQUİ, M , IMRAN, M , SAEED, M . (2020). Topological properties of face-centred cubic lattice. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 195-207 . DOI: 10.15672/hujms.546348
MLA SİDDİQUİ, M , IMRAN, M , SAEED, M . "Topological properties of face-centred cubic lattice". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 195-207 <https://dergipark.org.tr/en/pub/hujms/issue/52287/546348>
Chicago SİDDİQUİ, M , IMRAN, M , SAEED, M . "Topological properties of face-centred cubic lattice". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 195-207
RIS TY - JOUR T1 - Topological properties of face-centred cubic lattice AU - Muhammad Kamran SİDDİQUİ , Muhammad IMRAN , Muhammad SAEED Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.546348 DO - 10.15672/hujms.546348 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 195 EP - 207 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.546348 UR - https://doi.org/10.15672/hujms.546348 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Topological properties of face-centred cubic lattice %A Muhammad Kamran SİDDİQUİ , Muhammad IMRAN , Muhammad SAEED %T Topological properties of face-centred cubic lattice %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.546348 %U 10.15672/hujms.546348
ISNAD SİDDİQUİ, Muhammad Kamran , IMRAN, Muhammad , SAEED, Muhammad . "Topological properties of face-centred cubic lattice". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 195-207 . https://doi.org/10.15672/hujms.546348
AMA SİDDİQUİ M , IMRAN M , SAEED M . Topological properties of face-centred cubic lattice. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 195-207.
Vancouver SİDDİQUİ M , IMRAN M , SAEED M . Topological properties of face-centred cubic lattice. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 207-195.