ON CERTAIN TOPOLOGICAL INDICES OF NANOSTRUCTURES USINGQ(G) AND R(G) OPERATORS

Yıl 2018, Cilt: 67 Sayı: 2, 178 - 187, 01.08.2018

V. Lokesha R. Shrutı S. Ranjını P. A.sinan Cevık

Öz

The invention of new nanostructures gives a key measurement to
industry, electronics, pharmaceutical and biological therapeutics. By considering
the importance of this key point, in here we compute the 2D-lattice,
nanotube and nanotorus of TUC4C8[p; q] over the graphs Q(G) and R(G)
in terms of certain topological indices, namely Örst, second and third Zagreb
indices, hyper Zagreb index and forgotten topological index. These indices
are numerical propensity that often characterizes the quantitative structural
activity/property/toxicity relationships, and also correlates physico-chemical
properties such as boiling point, melting point and stability of respective nanostructures.

Anahtar Kelimeler

2D-lattice, nanotubes, nanotorus, first, second and third Zagreb indices, hyper Zagreb index, forgotten index

Kaynakça

• Ashra…, A. R., Youse…, S., Weiner index of a T U C4C8(s)nanotorus, MATCH Commun. Math. Comput. Chem. 57 (2007), 403-410.
• Ashra…, A. R., Ghorbani, M., Jalali, M., Computing Sadhana polynomial of V-phenylenic nanotubes and nanotori, Indian J. Chem. 47A (2008), 535-537.
• Diudea, M. V., Stefen, M., Parv, B., John, P. E., Wiener index of armchair polyhex nanotubes, Croat. Chem. Acta 77 (2004), 111-115.
• Diudea, M. V., Cigher, S., Vizitiu, A. E., Ursu, O., John, P. E., Omega polynomial tubular nanostructurer, Croat. Chem. Acta 79 (2006), 445-448.
• Fath-Tabar, M., Old and new Zagreb indices of graphs, MATCH Commun. Math. Comput. Chem. 65 (2011), 79-84.
• Furtula, B., Gutman, I., A forgotten topological index, J. Math. Chem. 53 (2015), 1184-1190.
• Furtula, B., Gutman, I., Vukicevic, Z. K., Lekishvili, G., Popivoda, G., On an old/new degree-based topological index, Bull. Acad. Serbe Sci. Arts (Cl. Sci. Math. Natur.) 148 (2015), 19-31.
• Gutman, I., Das, K. Ch., The …rst Zagreb indices 30 years after, MATCH Commun. Math. Comput. Chem. 50 (2004), 83-92.
• Gutman, I., Polansky, O., Mathematical concepts in organic chemistry, Springer-Verlag, Berlin, 1986.
• Hosamani, S. M., Zafar, S., On topological properties of the line graphs of subdivision graphs of certain nanostructures-II, Appl. Math. Comput. 273 (2016), 125-130.
• Ilic, A., Stevanovic, D., On comparing Zagreb indices, MATCH Commun. Math. Comput. Chem. 62 (2009), 681-687.
• John, P. E., Diudea, M. V., Wiener index of Zig-zag Polyhex Nanotubes, Croat. Chem. Acta. (2004), 127-132.
• Khalifeh, M. H., Youse…-Azari, H., Ashra…, A. R., The …rst and second Zagreb indices of some graph operations, Discr. Appl. Math. 157 (2009), 804-811.
• Lokesha, V., Usha, A., Ranjini, P. S., Devendraiah, K. M., Topological indices on model graph structure of Alveoli in human lungs, Proc. Jangjeon Math. Soc. 18 (2015), 435-453.
• Lokesha, V., Deepika, T., Ranjini, P. S., Cangul, I. N., Operations of nanostructures via SDD, ABC4, GA5indices, Appl. Math. Non-linear Sci. 2(1) (2017), 173-180.
• Nadeem, M. F., Zafar, S., Zahid, Z., On topological properties of the line graphs of subdivision graphs of certain nanostructures, Appl. Math. Comput. 273 (2016), 125-130.
• Nikolic, S., Kovacevic, G., Milicevic, A., Trinajstic, N., The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), 113-124.
• Ranjini, P. S., Lokesha, V., Rajan, M. A., On Zagreb indices of the subdivision graphs, Int. J. Math. Sc. Eng. Appl. 4 (2010), 221-228.
• Ranjini, P. S., Lokesha, V., Smarandache-Zagreb index on three graph operators, Int. J. Math. Combin. 3(2010), 1-10.
• Ranjini, P. S., Lokesha, V., On the Zagreb indices of the line graphs of the subdivision graphs, Appl. Math. Comput. 218 (2011), 699-702.
• Shirdel, G. H., Rezapour, H., Sayadi, A. M., The hyper Zagreb index of graph operations, Iran. J. Math. Chem. 4(2) (2013), 213-220.
• E-mail address : [e-mail] ORCID Address: http://orcid.org/0000-0003-2468-9511