### Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph

#### Abstract

Dutch windmill graph [1, 2] and denoted by *Dnm*. Order and size of Dutch windmill graph are (*n*−1)*m*+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, *M*-polynomials and some topological indices in term of the *M*-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.

#### Keywords

#### Full Text:

PDF#### References

Farahani, M. R., Jamil, M. K., Wang, S., Gao, W. and Wei, B. The hosoya, schultz and modified schultz polynomials of a class of Dutch windmill graph D(m)n , Communications in Applied Analysis 22(1): 43-62 (2017).

Rajesh Kanna, M. R., Pradeep Kumar, R. and Jagadeesh, R. Computation of topological indices of Dutch windmill graph, Open Journal of Discrete Mathematics 6: 74-81 (2016).

Devillers, J. and Balaban, A. T (Eds.). Topological indices and related descriptors in QSAR and QSPR, Gordon and Breach, Amsterdam, The Netherlands, (1999).

Gutman, I., Trinajsti´c, N. and Wilcox, C. F. Graph theory and molecular orbits. Total - electron energy of alternate hydrocarbons, Chem. Phys. Lett. 17: 535-538 (1972).

Khalifeh, M. H., Yousefi-Azari, H. and Ashrafi, A. R. The first and second Zagreb indices of some graph operations, Discrete. Appl. Math. 157: 804-811 (2009).

Deng, H., Sarala, D., Ayyaswamy, S. K. and Balachandran, S. The Zagreb index of four operations on graphs, Appl. Math. and comput. 275: 422-431 (2016).

Nabeel, A. E. Zagreb polynomials of certain families of bendrimer nanostars, Tikrit Journal of Pure Science 20(4): (2015).

Hao, J. Theorems about zagreb indices and modified zagreb indices, MATCH Commun. Math. Comput. Chem. 65: 659-670 (2011).

Shirdel, G.H., Rezapour, H. and Syadi, A. M. The hyper-Zagreb index of graph operations, Iranian J. Math.Chem. 4(2): 213-220 (2013).

Furtula, B. and Gutman, I. A forgotten topological index, J. Math. Chem. 53: 1184-1190 (2015).

Imran, M. and Akhter, S. The sharp bounds on general sum-connectivity index of four operations on graphs, J. Inequal. Appl. 241 (2016).

Gutman, I., Furtula, B. and Elphick, C. Three new/old vertex-degree based topological indices, MATCH Commun. Math. Comput. Chem. 72(24): 617-632 (2014).

Kulli, V. R. The gourava indices and coindices of graphs, Annals of Pure and Applied Mathematics 14(1): 33-38 (2017).

Kulli, V. R. The product connectivity gourava index, J. Comp. mMath. Sci. 8(6): 235-242 (2017).

Kulli, V. R. On the sum connectivity Gourava index, International Journal of Mathematical Archive 8(6): 211-217 (2017).

Kulli, V. R. On hyper-gourava indices and coindices, International Journal of Mathematical Archive 8(12): 116-120 (2017).

Ranjini, P.S., Lokesha, V. and Usha, A. Relation between phenylene and hexagonal squeeze using harmonic index. Int. J Graph Theory 1: 116-21 (2013).

Ahmad, M. S., Nazeer, W., Kang, S. M. and Jung, C. Y. M-polynomials and degree based topological indices for the line graph of Firecracker graph, Global Journal of Pure and Applied

Mathematics 13(6): 2749-2776 (2017).

Faisal Ndeem, M., Zafar, S. and Zahid, Z. On the certain topological indices of the line graph of subdivision graphs, Appl. Math. Comput. 217: 790-794 (2015).

Gao, Y., Jamil, M. K., Aslam, A. and Farahani, M. R. Comutation of some new/old vertex-degree-based topological indices of line graph of subdivision graph of some nanosrtuctures,

Journal of Optoelectronics and Biomedical Materials 9(3): 135-142 (2017).

Farahani, M. R., Jamil, M. K., Rajesh Kanna, M. R. and Hosamani, S. M. The wiener index and hosaya polynomial of the Subdivision Graph of wheel S(Wn) and the line graph subdivision of the wheel L(S(Wn)), Appl. Math. 6(2): 21-24 (2016).

Farahani, M. R. and Jamil, M. K. The schultz and modified schultz polynomials of the certain subdivision and line subdivision graphs, J. Chem. Pharm. Res. 8(3): 51-57 (2016).

Mahanappriya, G. and Vijayalakshmi, D. Topological indices of the total graph of subdivision graph, Annals of Pure and Applied Mathematics 14(2): 231-235 (2017).

Certain Topological Indices and Polynomials for the Semitotal-point Graph of Dutch Windmill Graph and its 1L5ine Graph

Ajmal, M., Nazeer, W., Khalid, W. and Kang, S. M. Forgotten polynomial and forgotten index for the line graphs of Banana tree graph, Firecracker graph and subdivision graphs, Global Journal of Pure and Applied Mathematics 13(6): 2673-2682 (2017).

Srinivasa, G. and Asha, K. Atom-bond connectivity index of subdivision graphs of some special graphs, International Journal of Advance Research in Computer Science 8(6): (2017).

Bertz, S. H. The bond graph, J. C. S. Chem. Commun.: 818-820 (1981).

Gutman, I. and Estrada, E. Topological indices based on the line graph of molecular graph, J. Chem. Inf. Comput. Sci. 36: 541 (1996).

Farahani, M. R., Faisal Nadeem, M., Zafar, S. and Husin, M. N. Study of the topological indices of the line graphs of H-pantacenic nanotubes, New FRONT. Chem. 26(1): 31-38 (2017).

DOI: http://dx.doi.org/10.19184/ijc.2019.3.2.1

#### References

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.