Topological invariants are the graph theoretical tools to the theoretical chemists, that correlates the molecular structure with several chemical reactivity, physical properties or biological activity numerically. A function having a set of networks(graph, molecular structure) as its domain and a set of real numbers as its range is referred as a topological invariant(index). Topological invariants are numerical quantity of a network that are invariant under graph isomorphism. Topological invariants such as Zagreb index, Randić index and multiplicative Zagreb indices are used to predict the bioactiviy of chemical compounds in QSAR/QSPR study. In this paper, we compute the general expression of certain degree based topological invariants such as second Zagreb index, F-index, Hyper-Zagreb index, Symmetric division degree index, irregularity of Splitting graph. And also we obtain upper bound for first and second multiplicative Zagreb indices of Splitting graph of a graph H, (S′(H)).

Topological invariant, degree based invariant, splitting graph.

- Albertson, M.O., The irregularity of a graph, Ars Combin., 46 (1997), 219-225.
- Basavanagoud and Shreekant, P., The Hyper-Zagreb index of four graph operations on graphs, Math. Sci. Lett., 6(2) (2017), 193-198.
- Furtula, B. and Gutman, I., A Forgotten topological index, J. Math. Chem., 53(4) (2015), 1184-1190.
- Gutman, I. and Trinajstic, N., Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17 (1972), 535-538.
- Ramane, H. S., Vinayak, V. M. and Ivan G., General sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of the line graph of subdivision graphs, AKCE Int. J. Graphs Comb., 14 (2017), 92-100.
- Imran, M. and Shenaz, A., Degree-based topological indices of double graphs and strong double graphs, Discrete Math. Algorithm. Appl., 9(5) (2017), 1750066-(1-15).
- Imran, M., Shakila, B., Hafiz, M.A. and Shafiq, M. K., On the bounds of degree-based topological indices of the cartesian product of F-sum of connected graphs, J. Inequal. Appl., (2017), 305(1-14).
- Sampath Kumar, E. and Walikar, H.B., On the Splitting graph of a graph, The Karnataka University Journal Science-vol XXV and XXVI (Combined)., (1980-1981), 13-16.
- Shenaz, A., and Imran, M., The sharp bounds on general sum-connectivity index of four graph operations on graphs, J. Inequal. Appl., (2016), 241(1-10).
- Shenaz, A. and Imran, M., Computing the forgotten topological index of four operations on graphs, AKCE Int. J. Graphs Comb., 14 (2017), 70-79.
- Shenaz, A., Imran, M. and Zahid, R., Bounds for the general sum-connectivity index of composite graphs, J. Inequal. Appl., (2017),76(1-12).
- Shirrdel, G.H., Rezapour, H. and Sayadi, A.M., The Hyper-Zagreb Indices of graph operations, Iranian J. Math. Chem.,4 (2013), 213-220.
- Todeschini, R., Ballabio, D. and Consonni, V., Novel molecular descriptors based on functions of the vertex degrees, Kragujevac J. Math., (2010), 73-100.
- Todeschini, R. and Consonni, V., New local vertex invariants and molecular descriptors based on functions of the vertex degrees , MATCH Commun. Math. Comput. Chem.,64 (2010), 359-372.
- Vukicevic, D., Bond additive modeling 2. mathematical properties of max-min rodeg index, Croat. Chem. Acta., 83(3) (2010), 261-273.
- Wiener, H., Structural determination of the paraffin boiling points, J. Amer. Chem. Soc., 69 (2010), 17-20.
- Odabaşı, Z. N. and Berberler, M. E., On the first Zagreb index of neighborhood corona graphs, J. Comput. Theor. Nanosci., 11(12) (2014), 2585-2587.

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Bibtex | ```
@araştırma makalesi { cfsuasmas526546,
journal = {Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics},
issn = {1303-5991},
eissn = {2618-6470},
address = {Ankara Üniversitesi},
year = {2019},
volume = {68},
pages = {1341 - 1349},
doi = {10.31801/cfsuasmas.526546},
title = {Degree based topological invariants of splitting graph},
key = {cite},
author = {Mohanappriya, G and Vijayalakshmi, D.}
}
``` |

APA | Mohanappriya, G , Vijayalakshmi, D . (2019). Degree based topological invariants of splitting graph. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68 (2), 1341-1349. DOI: 10.31801/cfsuasmas.526546 |

MLA | Mohanappriya, G , Vijayalakshmi, D . "Degree based topological invariants of splitting graph". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2019): 1341-1349 <http://dergipark.gov.tr/cfsuasmas/issue/42777/526546> |

Chicago | Mohanappriya, G , Vijayalakshmi, D . "Degree based topological invariants of splitting graph". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2019): 1341-1349 |

RIS | TY - JOUR T1 - Degree based topological invariants of splitting graph AU - G Mohanappriya , D. Vijayalakshmi Y1 - 2019 PY - 2019 N1 - doi: 10.31801/cfsuasmas.526546 DO - 10.31801/cfsuasmas.526546 T2 - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JF - Journal JO - JOR SP - 1341 EP - 1349 VL - 68 IS - 2 SN - 1303-5991-2618-6470 M3 - doi: 10.31801/cfsuasmas.526546 UR - http://dx.doi.org/10.31801/cfsuasmas.526546 Y2 - 2018 ER - |

EndNote | %0 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Degree based topological invariants of splitting graph %A G Mohanappriya , D. Vijayalakshmi %T Degree based topological invariants of splitting graph %D 2019 %J Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics %P 1303-5991-2618-6470 %V 68 %N 2 %R doi: 10.31801/cfsuasmas.526546 %U 10.31801/cfsuasmas.526546 |

ISNAD | Mohanappriya, G , Vijayalakshmi, D. . "Degree based topological invariants of splitting graph". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 / 2 (Temmuz 2019): 1341-1349. http://dx.doi.org/10.31801/cfsuasmas.526546 |