Topological properties of face-centred cubic lattice

Yıl 2020, Cilt: 49 Sayı: 1, 195 - 207, 06.02.2020

Muhammad Kamran Siddiqui , Muhammad Imran , Muhammad Saeed

https://doi.org/10.15672/hujms.546348

Cited By: 9

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 $FCC(n)$.

Anahtar Kelimeler

Randic index, atomic bond connectivity index, Zagreb types indices, Sanskruti index, 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.