Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 1, 195 - 207, 06.02.2020
https://doi.org/10.15672/hujms.546348

Öz

Kaynakça

  • [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.

Topological properties of face-centred cubic lattice

Yıl 2020, Cilt: 49 Sayı: 1, 195 - 207, 06.02.2020
https://doi.org/10.15672/hujms.546348

Öz

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 $FCC(n)$.

Kaynakça

  • [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.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Muhammad Kamran Siddiqui 0000-0002-2607-4847

Muhammad Imran 0000-0002-2827-0462

Muhammad Saeed Bu kişi benim 0000-0002-3296-5961

Yayımlanma Tarihi 6 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 1

Kaynak Göster

APA Siddiqui, M. K., Imran, M., & Saeed, M. (2020). Topological properties of face-centred cubic lattice. Hacettepe Journal of Mathematics and Statistics, 49(1), 195-207. https://doi.org/10.15672/hujms.546348
AMA Siddiqui MK, Imran M, Saeed M. Topological properties of face-centred cubic lattice. Hacettepe Journal of Mathematics and Statistics. Şubat 2020;49(1):195-207. doi:10.15672/hujms.546348
Chicago Siddiqui, Muhammad Kamran, Muhammad Imran, ve Muhammad Saeed. “Topological Properties of Face-Centred Cubic Lattice”. Hacettepe Journal of Mathematics and Statistics 49, sy. 1 (Şubat 2020): 195-207. https://doi.org/10.15672/hujms.546348.
EndNote Siddiqui MK, Imran M, Saeed M (01 Şubat 2020) Topological properties of face-centred cubic lattice. Hacettepe Journal of Mathematics and Statistics 49 1 195–207.
IEEE M. K. Siddiqui, M. Imran, ve M. Saeed, “Topological properties of face-centred cubic lattice”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, ss. 195–207, 2020, doi: 10.15672/hujms.546348.
ISNAD Siddiqui, Muhammad Kamran vd. “Topological Properties of Face-Centred Cubic Lattice”. Hacettepe Journal of Mathematics and Statistics 49/1 (Şubat 2020), 195-207. https://doi.org/10.15672/hujms.546348.
JAMA Siddiqui MK, Imran M, Saeed M. Topological properties of face-centred cubic lattice. Hacettepe Journal of Mathematics and Statistics. 2020;49:195–207.
MLA Siddiqui, Muhammad Kamran vd. “Topological Properties of Face-Centred Cubic Lattice”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 1, 2020, ss. 195-07, doi:10.15672/hujms.546348.
Vancouver Siddiqui MK, Imran M, Saeed M. Topological properties of face-centred cubic lattice. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):195-207.