The ``Forgotten Topological Index" of Double Corona of Graphs Related to the Different Subdivision Graphs

Yıl 2019, Cilt: 2 Sayı: 1, 8 - 15, 23.07.2019

Nilanjan De , Prosanta Sarkar Anita Pal

https://izlik.org/JA84AN58HU

Öz

Graph theory plays an important role in the chemical sciences to model chemical compounds graphically. A chemical graph is a representation of molecular structure whose vertices are considered as atoms of the molecule and edges are the bonds between them. A topological index is a numeric quantity associated with chemical compounds to predict various physicochemical properties and biological activities theoretically. The sum of the cube of degrees of all the vertices for a graph is called the ``forgotten topological index'' or F-index of that graph. In this study, we compute the F-index of double corona graphs related to the different subdivision graphs.

Anahtar Kelimeler

Forgotten topological index , Corona graph , $\mathcal{F}$-double corona of graphs

Kaynakça

• \bibitem[Gutman et al.(1972)]{gutm72}I. Gutman, N. Trinajesti\'{c}, \textit{Graph theory and molecular orbitals total $\pi$-electron energy of alternant hydrocarbons.} {Chem. Phys. Lett.}, 1972 (\textbf{17}): 535-538.
• \bibitem[Sarkar et al.(17)]{ndep17}P. Sarkar, N. De, and A. Pal, \textit{The Zagreb Indices of graphs based on new operations related to the join of graphs}. {J. Int. Math. Virtual Inst.}, (2017) (\textbf{7}): 181-209.
• \bibitem[De(16)]{nde16}N. De, \textit{The vertex Zagreb indices of some graphs operations}. {Carpathian Math. Publ.}, 2016 (\textbf{8}(2)): 215-223.
• \bibitem[Sarala et al.(17)]{sara17}D. Sarala, S.K. Ayyaswamy, and S. Balachandran, \textit{The Zagreb indices of graphs based on four new operations related to the lexicographic product}. {Appl. Math. Comput.}, 2017 (\textbf{309}): 156-169.
• \bibitem[De et al.(16)]{nay16}N. De, S.M.A. Nayeem, \textit{Computing the F-index of nanostar dendrimers}. {Pac. Sci. Rev. A: Nat. Sci. Engg.}, 2016 (\textbf{18}): 14-21.
• \bibitem[De(16)]{de16}N. De, \textit{F-index of four operations on graphs}. {Discrete Math. Algorithms Appl.}, 2016 (\textbf{8}(2)): 1-17 .
• \bibitem[Akhtar et al.(17)]{akh17}S. Akhtar, M. Imran, \textit{Computing the forgotten topological index of four operations on graphs}. {AKCE Int. J. Graphs Comb.}, 2017 (\textbf{14}(1)): 70-79.
• \bibitem[Gao et al.(16)]{wga16}W. Gao, M.K. Siddiqui, M. Imran, M.K. Jamil, and M.R. Farahani, \textit{Forgotten topological index of chemical structure in drugs}. {Saudi Phar. J.}, 2016 (\textbf{24}(3)): 258-264.
• \bibitem[Ranjini et al.(13)]{ranj13}P.S. Ranjini, V. Lokesha, and A. Usha, \textit{Relation between phenylene and hexagonal squeeze using harmonic index}. {Int. J. Graph Theory}, 2013 (\textbf{1}): 116-121.
• \bibitem[Gao et al.(16)]{gao16}W. Gao, M.R. Farahani, M.K. Jamil, and M.K. Siddique, \textit{The redefined first, second and third Zagreb indices of titania nanotubes $Ti{{O}_{2}}$[m,n]}. {Open Biotechnol. J.}, 2016 (\textbf{10}): 272-277.
• \bibitem[Kumar et al.(17)]{kum17}R.P. Kumar, D.S. Nandappa, and M.R.R. Kanna, \textit{Redefined Zagreb, randic, harmonic and GA indices of graphene}. {Int. J. Math. Anal.}, 2017 (\textbf{11}): 493-502.
• \bibitem[Farahani et al.(16)]{farah16}M.R. Farahani, W. Gao, \textit{On multiplicative and redefined version of Zagreb indices of V-phenylenic nanotubes and nanotorus}. {British J. Math. Comput. Sci.}, 2016 (\textbf{13}(5): 1-8.
• \bibitem[Shirrdel et al.(13)]{shir13}G.H. Shirrdel, H. Rezapour, A.M. Sayadi, \textit{The hyper Zagreb index of graph operations}. {Iran. J. Math. Chem.}, 2013 (\textbf{4}): 213-220 .
• \bibitem[De(18)]{ndeh18}N. De, \textit{Hyper Zagreb index of bridge and chain graphs}. {Open J. Math. Sci.}, 2018 (\textbf{2}(1)): 1-17.
• \bibitem[Gao et al.(17)]{gao17}W. Gao, M.K. Jamil, and M.R. Farahani, \textit{The hyper-Zagreb index and some graph operations}. {J. Appl. Math. Comput.}, 2017 (\textbf{54}): 263-275.
• \bibitem[Barik et al.(17)]{bar17}S. Barik, G. Sahoo, \textit{On the Laplacian spectra of some variants of corona}. {Linear Algebra Appl.}, 2017 (\textbf{512}): 32-47.