Topological Indices for Inverse Graphs Associated With Finite Cyclic Group




Hosoya polynomial, Wiener index, Hyper-Wiener index, Inverse graph


Topological indices are mathematical descriptors for molecular structures. These descriptors are used to describe physico-chemical properties such as solubility, molecular shape and molecular weight. In this paper, we present distance-based topological indices such as Wiener index and hyper-Wiener index by using Hosoya polynomial for inverse graphs associated with finite cyclic group. Also, we have found eccentricity based topological index of inverse graphs associated with finite cyclic group.


Download data is not yet available.


M. R. Alfuraidan and Y. F. Zakariya, Inverse graphs associated with finite groups, Electronic Journal of Graph Theory and Applications 5(1) (2017), 142 – 154, DOI: 10.5614/ejgta.2017.5.1.14

M. R. Alfuraidan, G. Kalaimurugan and P. Vignesh, On the genus of the inverse graphs of finite abelian groups, Rundschau 119 (2021), 30 – 39.

A. Ayache and A. Alameri, Topological indices of the mk -graph, Journal of the Association of Arab Universities for Basic and Applied Sciences 24(1) (2017), 283 – 291, DOI: 10.1016/j.jaubas.2017.03.001.

J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Elsevier, North Holland – Amsterdam (1986).

G. G. Cash, Relationship between the Hosoya polynomial and the hyper-Wiener index, Applied Mathematics Letters 15(7) (2002), 893 – 895, DOI: 10.1016/S0893-9659(02)00059-9.

O. Ejima, K. O. Aremu and A. Audu, Energy of inverse graphs of dihedral and symmetric groups, Journal of the Egyptian Mathematical Society 28 (2020), Article number: 43, DOI: 10.1186/s42787-020-00101-8.

M. Ghorbani and M. A. Hosseinzadeh, A new version of Zagreb index, Filomat 26(1) (2012), 93 – 100, DOI: 10.2298/FIL1201093G

I. Gutman, S. Klavžar, M. Petkovšek and P. Žigert, On Hosoya polynomials of benzenoid graphs, MATCH Communications in Mathematical and in Computer Chemistry 43 (2001), 49 – 66,

H. Hosoya, On some counting polynomials in chemistry, Discrete Applied Mathematics 19(1–3) (1988), 239 – 257, DOI: 10.1016/0166-218X(88)90017-0.

J.-B. Liu, I. Khalid, M. T. Rahim, M. Ur Rehman, F. Ali and M. Salman, Eccentric topological properties of a graph associated to a finite dimensional vector space, Main Group Metal Chemistry 43(1) (2020), 164 – 176, DOI: 10.1515/mgmc-2020-0020.

K. Mageshwaran, G. Kalaimurugan, B. Hammachukiattikul, V. Govindan and I. N. Cangul, On L(h,k)-labeling index of inverse graphs associated with finite cyclic groups, Journal of Mathematics 2021 (2021), Article ID 5583433, DOI: 10.1155/2021/5583433.

K. Mageshwaran, N. Alessa, S. Gopinath and K. Loganathan, Topological indices of graphs from vector spaces, Mathematics 11(2) (2023), 295, DOI: 10.3390/math11020295.

N. Trinajstic, Chemical Graph Theory, 2nd Edition, CRC Press, Boca Raton (1992), DOI: 10.1201/9781315139111.

R. Xing, B. Zhou and F. Dong, On atom–bond connectivity index of connected graphs, Discrete Applied Mathematics 159(15) (2011), 1617 – 1630, DOI: 10.1016/j.dam.2011.06.004.




How to Cite

Gopinath, S., Doss, A. R. P., & Kalaimurugan, G. (2023). Topological Indices for Inverse Graphs Associated With Finite Cyclic Group. Communications in Mathematics and Applications, 14(1), 415–427.



Research Article