<abstract xmlns="http://www.w3.org/1999/xhtml">Recently, nanostructures have opened new dimensions in industry, electronics, and pharmaceutical and biological therapeutics. The topological indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties such as boiling point, stability, and strain energy, of respective nanomaterial. In this article, we established closed forms of various degree-based topological indices of semi-total line graph of 2D-lattice, nanotube and nanotorus of <italic>TUC</italic>4<italic>C</italic>8[<italic>r</italic>, <italic>s</italic>].</abstract>

Recently, nanostructures have opened new dimensions in industry, electronics, and pharmaceutical and biological therapeutics. The topological indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties such as boiling point, stability, and strain energy, of respective nanomaterial. In this article, we established closed forms of various degree-based topological indices of semi-total line graph of 2D-lattice, nanotube and nanotorus of TUC4C8[r, s].

Operations of Nanostructures via <italic>SDD</italic>, <italic>ABC</italic>4 and <italic>GA</italic>5 indices

Vijayanagara Sri Krishnadevaraya University

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Operations of Nanostructures via ,  and  indices

Recently, nanostructures have opened new dimensions in industry, electronics, and pharmaceutical and biological therapeutics. The topological indices are...

(a) r > 1 and s = 1
Edges Partitioned	(2,4)	(2,5)	(3,5)	(3,6)	(4,4)	(4,5)	(5,5)	(5,6)
No of Edges	8	4(r-1)	4(r-1)	2(r-1)	2	4	2(2r-3)	4(r-1)

(a) r > 1 and s = 1
Edges Partitioned	No of Edges
(8,13) (9,13) (13,20) (9,20) (16,20) (20,26)	4
(13,13) (20,20)	2
(16,26)	2(r-1)
(16,21) (10,21) (21,21) (21,26)	4(r-2)

(a) r > 1 and s = 1
Edges Partitioned	(3,3)	(3,6)	(6,6)
No of Edges	2(r + 1)	2(7r + 1)	4(2r − 1)

(a) r > 1 and s = 1
Edges Partitioned	No of Edges
(15,24)	16
(24,27)	4
(24,24)	2
(15,15)	2(r + 1)
(15,27)	8(r − 1)
(27,27)	2(2 r − 3)
(18,30)	2(r − 1)
(27,30) (18,27)	4(r − 1)

(a) r > 1 and s = 1
Edges Partitioned	(2,5)	(3,3)	(3,5)	(5,5)	(5,6)
No of Edges	4r	2	4(r+1)	2(r-1)	4r	4(r-1)

Operations of Nanostructures via SDD, ABC₄ and GA₅ indices

Pubblicato online: 16 mag 2017

Pagine: 173 - 180

Ricevuto: 07 mar 2017

Accettato: 16 mag 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00014

Parole chiave
Topological indices, 2-lattice, nanotube, nanotorus, semi-total line operator

© 2017 V. Lokesha, T. Deepika, P. S. Ranjini, I. N. Cangul, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Figure 2

Figure 3

Edge partition of Semi-total(line) graph of 2D-Lattice

Edge Partition of Semi-total(line) graph of 2D-Lattice for Neighborhood vertices

Edge Partition for Semi-total(line) graph of Nanotorus

Semi-total(line) graph of Nanotorous for Neighborhood vertices

Semi-total line graph of nanotube

Semi-total(line) graph of Nanotube for Neighborhood vetices

Operations of Nanostructures via SDD, ABC4 and GA5 indices

Pubblicato online: 16 mag 2017

Pagine: 173 - 180

Ricevuto: 07 mar 2017

Accettato: 16 mag 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00014

Parole chiaveTopological indices, 2-lattice, nanotube, nanotorus, semi-total line operator

© 2017 V. Lokesha, T. Deepika, P. S. Ranjini, I. N. Cangul, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Figure 2

Figure 3

Edge partition of Semi-total(line) graph of 2D-Lattice

Edge Partition of Semi-total(line) graph of 2D-Lattice for Neighborhood vertices

Edge Partition for Semi-total(line) graph of Nanotorus

Semi-total(line) graph of Nanotorous for Neighborhood vertices

Semi-total line graph of nanotube

Semi-total(line) graph of Nanotube for Neighborhood vetices

Operations of Nanostructures via SDD, ABC₄ and GA₅ indices

Parole chiave
Topological indices, 2-lattice, nanotube, nanotorus, semi-total line operator