On topological properties of boron triangular sheet BTS(m,n), borophene chain B36(n) and melem chain MC(n) nanostructures

Authors

1 Government College University Faisalabad Pakistan

2 Department of Mathematics, COMSATS Institute of Information Technology, Attock Campus, Pakistan

3 Department of Mathematics,Government College University, Faisalabad, Pakistan

Abstract

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randic, atom-bond connectivity ´ (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study and derive analytical closed results of general Randic index ´ Rα(G) with α = 1, 1 2 ,−1,−1 2 , for boron triangular sheet BTS(m,n), borophene chain of B36(n) and melem chain MC(n). We also compute the general first Zagreb, ABC, GA, ABC4 and GA5 indices of sheet and chains for the first time and give closed formulas of these degree based indices.

Graphical Abstract

On topological properties of boron triangular sheet BTS(m,n), borophene chain B36(n) and melem chain MC(n) nanostructures

Keywords

Main Subjects


[1] H. Ali, A. Q. Baig, M. K. Shafiq, On topological properties of hierarchical interconnection networks, J. Appl. Math. Comput. 55 (1-2) (2017) 313–334.

[2] M. Baca, J. Horv ˇ athov ´ a, M. Mokri ´ sov ˇ a, A. Suh ´ anyiov ´ a, On topological indices of fullerenes, Appl. ˇ Math. Comput. 251 (2015) 154–161.

[3] A. Q. Baig, M. Imran, H. Ali, Computing Omega, Sadhana and PI polynomials of benzoid carbon nanotubes, OAM-RC. 9 (2015) 248–255.

[4] A. Q. Baig, M. Imran, H. Ali, On Topological Indices of Poly Oxide, Poly Silicate, DOX and DSL Networks, Can. J. Chem. 93 (2015) 1–10.

[5] M. Deza, P. W. Fowler, A. Rassat, K. M. Rogers, Fullerenes as tiling of surfaces, J. Chem. Inf. Comput. Sci. 40 (2000) 550–558.

[6] M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova, Huntington, 2001.

[7] E. Estrada, L. Torres, L. Rodr´ıguez, I. Gutman, An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes, Indian J. Chem. 37A (1998) 849–855.

[8] M. Ghorbani, M. A. Hosseinzadeh, Computing ABC4 index of nanostar dendrimers, Optoelectron. Adv. Mater. Rapid Commun. 4 (2010) 1419–1422.

[9] A. Graovac, M. Ghorbani, M. A. Hosseinzadeh, Computing fifth geometric-arithmetic index for nanostar dendrimers, J. Math. Nanosci. 1 (2011) 33–42.

[10] I. Gutman, O. E. Polansky, Mathematical concepts in organic chemistry, Springer-Verlag, New York, 1986.

[11] S. Hayat, M. Imran, Computation of certain topological indices of nanotubes, J. Comput. Theor. Nanosci. 12 (2015) 70–76.

[12] S. Hayat, M. Imran, Computation of topological indices of certain networks, Appl. Math. Comput. 240 (2014) 213–228.

[13] M. Imran, A. Q. Baig, H. Ali, On topological properties of dominating David derived graphs, Can. J. Chem. 94 (2016) 137–148.

[14] M. Imran, A. Q. Baig, H. Ali, On molecular topological properties of hex-derived graphs, J. Chemometrics, 30 (2016) 121–129.

[15] M. Imran, A. Q. Baig, H. Ali, S. U. Rehman, On topological properties of poly honeycomb graphs, Period Math Hung, 73 (2016) 100–119.

[16] A. Iranmanesh, M. Zeraatkar, Computing GA index for some nanotubes, Optoelectron. Adv. Mater. Rapid Commun. 4 (2010) 1852–1855.

[17] W. Lin, J. Chen, Q. Chen, T. Gao, X. Lin, B. Cai, Fast computer search for trees with minimal ABC index based on tree degree sequences, MATCH Commun. Math. Comput. Chem. 72 (2014) 699–708.

[18] P. D. Manuel, M. I. Abd-El-Barr, I. Rajasingh, B. Rajan, An efficient representation of Benes networks and its applications, J. Discrete Algorithms, 6 (2008) 11–19.

[19] J. L. Palacios, A resistive upper bound for the ABC index, MATCH Commun. Math. Comput. Chem. 72 (2014) 709–713.

[20] M. Randic, On Characterization of molecular branching, J. Amer. Chem. Soc. 97 (1975) 6609–6615. ´

[21] F. Simonraj, A. George, Embedding of poly honeycomb networks and the metric dimension of star of david network, GRAPH-HOC, 4 (2012) 11–28.

[22] F. Simonraj, A. George, Topological Properties of few Poly Oxide, Poly Silicate, DOX and DSL Networks, International Journal of Future Computer and Communication, 2 (2013) 90–95.

[23] D. Vukicevi ˇ c B. Furtula, Topological index based on the ratios of geometrical and arithmetical ´ means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376.

[24] H. Wiener, Structural determination of paraffin boiling points, J. Amer. Chem. Soc. 69 (1947) 17–20.