On the F-index and F-coindex of the line graphs of the subdivision graphs
Downloads
DOI:
https://doi.org/10.26637/MJM0602/0010Abstract
The aim of this work is to investigate the F-index and F-coindex of the line graphs of the cycle graphs, star graphs, tadpole graphs, wheel graphs and ladder graphs using the subdivision concepts. F-index of the line graph of subdivision graph of square grid graph, 2D-lattice, nanotube and nanotorus of $T U C_4 C_8[p, q]$ are also investigated here.
Keywords:
Topological index, F-index, F-coindex, line graphs, subdivision graphs, cycle graph, star graph, square grid graph, tadpole graphs, wheel graphs, ladder graphs, 2D-lattice of $ T U C_4 C_8[p, q]$, nanotube of $T U C_4 C_8[p, q]$, nanotorus of $ T U C_4 C_8[p, q]$Mathematics Subject Classification:
Mathematics- Pages: 362-368
- Date Published: 01-04-2018
- Vol. 6 No. 02 (2018): Malaya Journal of Matematik (MJM)
H. Abdo, D. Dimitrov and I. Gutman, On extremal trees with respect to the F-index, Kuwait J. Sci. 44(3)(2017) 1 8.
R. Amin and S.M.A. Nayeem, Trees with minimum Fcoindex, Electronic Notes Disc. Math. 63(2017) 303-310.
N. De, S.M.A. Nayeem and A. Pal, F-index of some graph operations, Disc. Math. Alg. Appl. 8, $1650025(2016)$ [17 pages] doi: $10.1142 / mathrm{S} 1793830916500257$.
N. De, S.M.A. Nayeem and A. Pal, The F-coindex of some graph operations, SpringerPlus 5(2016) [13 pages] doi: $10.1186 / s 40064-016-1864-7$.
T. Došlić, Vertex-weighted wiener polynomials for composite graphs, Ars Math. Contemp. 1(2008) 66-80.
M.R. Farahani, M.F. Nadeem, S. Zafar, Z. Zahid and M.N. Husin, Study of the topological indices of the line graphs of H-pantacenic nanotubes, New Front. Chem. $26(1)(2017) 31-38$.
B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53(2015) 1184-1190.
Y. Gao, M.F. Nadeem, S. Zafar, Z. Zahid, M.N. Husin and M.R. Farahani, About the certain topological indices of the line graph of V-pantacenic nanotube, Int. J. Pharma. Sci. Res. 8(12)(2017) 5354-5352.
I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $varphi$-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17(1972) 535-538.
I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86(2013) 351-361.
S.M. Hosamani, On topological properties of the line graphs of subdivision graphs of certain nanostructures - II, Global J. Sci. Front. Res. F: Math. Decision Sci. $17(4)(2017) 39-47$
Y. Hu, X. Li, Y. Shi, T. Xu and I. Gutman, On molecular graphs with smallest and greatest zeroth-order general Randić index, MATCH Commun. Math. Comput. Chem. $54(2005) 425-434$.
Y. Huo, J.B. Liu, Z. Zahid, S. Zafar, M.R. Farahani and M.F. Nadeem, On certain topological indices of the line graph of $mathrm{CNC}_k[n]$ nanocones. J. Comput. Theor. Nanosci. $13(2016) 4318-4322$.
A. Islam, J.L. Garcia Guirao, S Ahmad and W. Gao, Topological indices of the line graph of subdivision graph of complete bipartite graphs, Appl. Math. Inf. Sci. $11(6)(2017) 1631-1636$
X. Li and H. Zhao, Trees with the first three smallest and largest generalized topological indices, MATCH Commun. Math. Comput. Chem. 50(2004) 57-62.
X. Li and J. Zheng, A unified approach to the extremal trees for different indices, MATCH Commun. Math. Comput. Chem. 54(2005) 195-208.
M.F. Nadeem, S. Zafar and Z. Zahid, On certain topological indices of the line graph of subdivision graphs, Appl. Math. Comput. 271(2015) 790-794.
M.F. Nadeem, S. Zafar and Z. Zahid, On topological properties of the line graphs of subdivision graphs of certain nanostructures, Appl. Math. Comput. 273(2016) 125-130.
P.S. Ranjini, V. Lokesha and I.N. Cangul, On the Zagreb indices of the line graphs of the subdivision graphs, Appl. Math. Comput. 218(2011) 699-702 .
G. Su and L. Xu, Topological indices of the line graph of subdivision graphs and their Schur-bounds, Appl. Math. Comput. 253(2015) 395-401.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.