On leap Zagreb indices of some nanostructures

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DOI:

https://doi.org/10.26637/MJM0604/0018

Abstract

In recent years, higher order topological indices are gaining much importance because of their greater correlation with many chemical properties. One among them is leap Zagreb index which is based on both distance and degree. For a graph $G$, the first, second and third leap Zagreb indices are the sum of squares of 2-distance degree of vertices of $G$; the sum of product of 2-distance degree of end vertices of edges in $G$ and the sum of product of 1-distance degree and 2-distance degrees of vertices of $G$, respectively. In this paper, we compute the expressions for these three leap Zagreb indices of some nanostructures.

Keywords:

distance, leap Zagreb index, Degree, nanostructure

Mathematics Subject Classification:

Mathematics
  • Pages: 816-822
  • Date Published: 01-10-2018
  • Vol. 6 No. 04 (2018): Malaya Journal of Matematik (MJM)

A. R. Ashrafi and A. Loghman, PI index of armchair polyhex nanotubes, Ars Combinatoria, 80(2006), 193.

A. Bahrami, J. Yazdani, Vertex PI index of V-phenylenic nanotubes and nanotori, Digest J. Nanomaterials and Biostructures, 4(1)(2009), 141-144.

B. Basavanagoud, S. Patil and H. Deng,On the second order first Zagreb index, Iranian J. Math. Chem., $8(3)(2017), 299-311$.

B. Basavanagoud, V. R. Desai and S. Patil, $(beta, alpha)-$ connectivity index of graphs, Appl. Math. Nonlinear Sci., $2(1)(2017), 21-30$

H. Deng, Catacondensed benzenoids and phenylenes with the extremal third order Randic index, MATCH Commun. Math. Comput. Chem., 64(2010), 471-496.

M. R. Farahani, Computing $G A_5$ index of V-phenylenic nanotubes and nanotori, Int. J. Chem. Model., 5(1)(2014), $479-484$.

M. R. Farahani, Computing theta polynomial and theta index of V-phenylenic planar, nanotubes and nanotoris, Int. J. Theoretical Chem., 1(1)(2013), 01-09.

B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem., 53(2015), 1184-1190.

I. Gutman and N. Trinajstić, Graph theory and molecular orbitals, Total $pi$ electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17(1972), 535-538.

F. Harary, Graph Theory, Addison-Wesely, Reading, Mass, 1969.

S. M. Hosamani, Computing Sanskruti index of certain nanostructures, J. Appl. Math. Comput., (2016) DOI. 10.1007/s12190-016-1016-9.

A. Heydari and B. Taeri, Szeged index of nanotubes, MATCH Commun. Math. Comput. Chem., 57(2007), 463477.

A. Heydari and B. Taeri, Wiener and Schultz indices of TUC4C8(S) nanotubes, MATCH. Commun. Math. Comput. Chem., 57(2007), 665-676.

H. Jiang, M. S. Sardar, M. R. Farahani , M. Rezaei and M. K. Siddiqui, Computing Sanskruti index of Vphenylenic nanotubes and nanotori, Int. J. pure Appl. Math., 115(4)(2017), 859-865.

K. G. Mirajkar and Y. B. Priyanka, On the reformulated Zagreb indices of certain nanostructures, Global J. Pure Appl. Math., 13(2)(2017), 817-827.

V. R. Kulli, College Graph Theory , Vishwa Int. Publ., Gulbarga, India, 2012.

A. M. Naji, N. D. Soner and I. Gutman, On leap Zagreb indices of graphs, Commun. Comb. Optim., 2(2)(2017), 99-117.

M. J. Nikmehr, M. Veylaki and N. Soleimani, Some topological indices of V-phenylenic nanotube and nanotori, Optoelectron Adv. Mater-Rapid Comm., 9(9)(2015), 1147-1149.

N. Soleimani, M. J. Nikmehr and H. A. Tavallae, Computation of the different topological indices of nanostructures, J. Natn. Sci. Foundation Sri Lanka, 43(2)(2015), 127-133.

N. Soleimani, E. Mohseni, F. Rezaei and F. Khati, Some formulas for the polynomials and topological indices of nanostructures, Acta Chem. Iasi, 24(2)(2016), 122-138.

N. D. Soner and A. M. Naji, The k-distance neighbourhood polynomial of a graph, Int. J. Math. Comput. Sci. WASET Conference Proceedings, 3(9)part XV(2016), $2359-2364$.

H. Wiener, Strucural determination of paraffin boiling points, J. Amer. Chem. Soc., 69(1947), 17-20.

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Published

01-10-2018

How to Cite

B. Basavanagoud, and E. Chitra. “On Leap Zagreb Indices of Some Nanostructures”. Malaya Journal of Matematik, vol. 6, no. 04, Oct. 2018, pp. 816-22, doi:10.26637/MJM0604/0018.