### Application of generalised hierarchical product of graphs for computing F-index of four operations on graphs

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total pi-electron energy of alternant hydrocarbons, Chemical Physics Letters, 17 (1972) 535-538.

K. Xu, K. Tang, H. Liu and J. Wang, The Zagreb indices of bipartite graphs with more edges, Journal of Applied Mathematics and Informatics, 33 (2015) 365-377.

K.C. Das, K. Xu and J. Nam, On Zagreb indices of graphs, Frontiers of Mathematics in China, 10 (2015) 567--582.

M.H. Khalifeha, H. Yousefi-Azaria and A.R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Applied Mathematics, 157(4) (2009) 804-811.

B. Zhou, Upper bounds for the Zagreb indices and the spectral radius of series-parallel graphs, International Journal of Quantum Chemistry, 107 (2007) 875–878.

B. Zhou, I. Gutman, Further properties of Zagreb indices, MATCH. Communications in Mathematical and in Computer, 54 (2005) 233-239.

B. Furtula, I. Gutman, A forgotten topological index, Journal of Mathematical Chemistry, 53(4) (2015) 1184--1190.

N. De, S.M.A. Nayeem and A. Pal, F-index of some graph operations, Discrete Mathematics, Algorithms and Applications, 8(2) (2016), doi :10.1142/S1793830916500257.

N. De, S.M.A. Nayeem and A. Pal, The F-coindex of some graph operations, SpringerPlus, 5:221, (2016), doi: 10.1186/s40064-016-1864-7.

N. De, S.M.A. Nayeem, Computing the F-index of nanostar dendrimers, Pacific Science Review A: Natural Science and Engineering, doi:10.1016/j.psra.2016.06.001.

B. Furtula, I. Gutman, Ž.K. Vukicevic, G. Lekishvili and G. Popivoda, On an old/new degree-based topological index, textit{Bulletin de l'Académie Serbe des Sciences et des Arts (Cl. Math. Natur.)}, 40 (2015) 19–31.

H. Abdoa, D. Dimitrov and I. Gutman, On extremal trees with respect to the F-index, arXiv:1509.03574v2.

X. Li, J. Zheng, A unified approach to the extremal trees for different indices, MATCH. Communications in Mathematical and in Computer, 54 (2005) 195–-208.

S. Zhang, W. Wang and T.C.E. Cheng, Bicyclic graphs with the first three smalllest and largest values of the first general Zagreb index, MATCH. Communications in Mathematical and in Computer, 55 (2006) 579–-592.

H. Zhang, S. Zhang, Unicyclic graphs with the first three smallest and largest first general Zagreb index, MATCH. Communications in Mathematical and in Computer, 55 (2006) 427–-438.

I. Gutman, An exceptional property of the first Zagreb index, MATCH. Communications in Mathematical and in Computer, 72 (2014) 733–-740.

X. Li, H. Zhao, Trees with the first smallest and largest generalized topological indices, MATCH. Communications in Mathematical and in Computer, 50 (2004) 57–-62.

P.S. Ranjini, V. Lokesha and A. Usha, Relation between phenylene and hexagonal squeeze using harmonic index, International Journal of Graph Theory, 1 (2013) 116--121.

P.S. Ranjini, A. Usha, V. Lokesha and T. Deepika, Harmonic index, redefined Zagreb indices of dragon graph with complete graph, Asian Journal of Mathematics and Computer Research, 9(2) (2016) 161--166.

W. Gao, W. Wang and M.R. Farahani, Topological Indices Study of Molecular Structure in Anticancer Drugs, Journal of Chemistry, (2016), http://dx.doi.org/10.1155/2016/3216327.

X. Xu, Relationships between harmonic index and other topological indices, Applied Mathematical Sciences, 6(41) (2012) 2013--2018.

L. Barriere, F. Comellas, C. Dalfo and M. A. Fiol, The hierarchical product of graphs, Discrete Applied Mathematics, 157 (2009) 36--48.

L. Barri`{e}re, C. Dalf'{o}, M. A. Fiol and M. Mitjana, The generalized hierarchical product of graphs, textit{Discrete Mathematics}, 309 (2009) 3871--3881.

M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Applied Mathematics, 157 (2009) 794--803.

M. Arezoomand, B. Taeri, Applications of generalized hierarchical product of graphs in computing the Szeged index of chemical graphs, MATCH. Communications in Mathematical and in Computer, 64(3) (2010) 591--602.

M. Eliasi, A. Iranmanesh, Hosoya polynomial of hierarchical product of graphs, MATCH. Communications in Mathematical and in Computer, 69(1) (2013) 111--119.

M. Arezoomand, B. Taeri, Zagreb indices of the generalized hierarchical product of graphs, MATCH. Communications in Mathematical and in Computer, 69(1) (2013) 131--140.

Z. Luo, J. Wu, Zagreb Eccentricity Indices of the Generalized Hierarchical Product Graphs and Their Applications, Journal of Applied Mathematics, 2014(2014), Article ID 241712, 8 pages, http://dx.doi.org/10.1155/2014/241712 2014.

N. De, S.M.A. Nayeem and A. Pal, Total eccentricity index of generalized hierarchical product of graphs, International Journal of Applied and Computational Mathematics, (2014), doi: 10.1007/s40819-014-0016-4.

S. Li, G. Wang, Vertex PI indices of four sums of graphs, Discrete Applied Mathematics, 159 (2011) 1601–-1607.

M. Metsidik, W. Zhang, F. Duan, Hyper and reverse Wiener indices of F-sums of graphs, Discrete Applied Mathematics, 158 (2010) 1433--1440.

B. Eskender, E. Vumar, Eccentric connectivity index and eccentric distance sum of some graph operations, Transactions on Combinatorics, 2(1) (2013) 103--111.

M. An, L. Xiong and K.C. Das, Two Upper Bounds for the Degree Distances of Four Sums of Graphs, Filomat, 28(3) (2014) 579–-590.

H. Deng, D. Sarala, S.K. Ayyaswamy and S. Balachandran, The Zagreb indices of four operations on graphs, Applied Mathematics and Computation, 275 (2016) 422-–431.

N. De, A. Pal, and S.M.A. Nayeem, The irregularity of some composite graphs, International Journal of Applied and Computational Mathematics, DOI 10.1007/s40819-015-0069-z.

N. De, A. Pal, and S.M.A. Nayeem, Total eccentricity index of some composite graphs, Malaya Journal of Matematik, 3(4)(2015) 523-529.

W. Yan, B.Y. Yang and Y.N. Yeh, The behavior of Wiener indices and polynomials of graphs under five graph decorations, Applied Mathematics Letter, 20 (2007) 290--295.

DOI: http://dx.doi.org/10.19184/ijc.2018.2.2.5

### Refbacks

- There are currently no refbacks.

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