Entire forgotten topological index of graphs
DOI:
https://doi.org/10.22199/issn.071762792020040064Keywords:
Degree of vertex, Zagreb indices, Findex, Operations of graphsAbstract
The Forgotten topological index or Findex is defined as the sum of cubes of the degrees of vertices of a graph. For this classical Findex, we ignore the intermolecular forces that exist between the atoms and bonds and consider only the intermolecular forces between the atoms of a molecule. In this paper, we introduce a new graph invariant called “Entire Forgotten topological index” or “Entire Findex”, that includes incidency of edges and vertices in addition to the adjacency of the vertices. We obtain some important properties of the index and also establish formulae of this newly defined index for some operations of graphs.
References
S. Akhtar and M. Imran, “Computing the forgotten topological index of four operations on graphs”, AKCE international journal of graphs and combinatorics, vol. 14, no. 1, pp. 7079, 2017, doi: 10.1016/j.akcej.2016.11.012
A. Alwardi, A. Alqesmah, R. Rangarajan, and I. N. Cangul, “Entire Zagreb indices of graphs”, Discrete mathematics, algorithms and applications, vol. 10, no. 3, Art ID. 1850037, 2018, doi: 10.1142/S1793830918500374
B. Basavanagoud, S. Patil, V. R. Desai, and S. M. Hosamani, “Computing certain topological indices of InduBala product of graphs”, 2016. [On line]. Available: https://bit.ly/3e8IsvK
J. Buragohain, B. Deka, and A. Bharali, “A generalized ISI index of some chemical structures”, Journal of molecular structure, vol. 1208, Art ID. 127843, May 2020, doi: 10.1016/j.molstruc.2020.127843
D. M. Cvetković, M. Doob, and H. Sachs, Spectra of graphs: theory and application. New York, NY: Academic Press, 1980.
H. Deng, D. Sarala, S. K. Ayyaswamy, and S. Balachandran, “The Zagreb indices of four operations on graphs”, Applied mathematics and computation, vol. 275, pp. 422431, Feb. 2016, doi: 10.1016/j.amc.2015.11.058
M. V. Diudea and I. Gutman, “WienerType topological indices”, Croatica chemica acta, vol. 71, no. 1, pp. 2151, 1998. [On line]. Available: https://bit.ly/3ffYPYN
C. M. da Fonseca and D. Stevanović, “Further properties of the second Zagreb index”, MATCH communications in mathematical and in computer chemistry, vol. 72, no. 3, pp. 655668, 2014. [On line]. Available: https://bit.ly/2OcXx4J
B. Furtula and I. Gutman, “A forgotten topological index”, Journal of mathematical chemistry, vol. 53, no. 4, pp. 11841190, Apr. 2015, doi: 10.1007/s109100150480z
I. Gutman and B. Furtula, Ž. K. Vukićević, and G. Popivoda, “On Zagreb indices and coindices”, MATCH communications in mathematical and in computer chemistry, vol. 74, no. 1, pp. 516, 2015. [On line]. Available: https://bit.ly/32ekHAf
I. Gutman, “Degreebased topological indices”, Croatica chemica acta, vol. 86, no. 4, pp. 351361, 2013, doi: 10.5562/cca2294
I. Gutman and K. C. Das, “The first Zagreb index 30 years after”, MATCH communications in mathematical and in computer chemistry, vol. 50, pp. 8392, 2004. [On line]. Available: https://bit.ly/2B5AEwS
I. Gutman and N. Trinajstić, “Graph theory and molecular orbitals. Total φelectron energy of alternant hydrocarbons”, Chemical physics letters, vol. 17, no. 4, pp. 535–538, Dec. 1972, doi: 10.1016/00092614(72)850991
G. Indulal and R. Balakrishnan, “Distance spectrum of InduBala product of graphs”, AKCE international journal of graphs and combinatorics, vol. 13, no. 3, pp. 230234, 2016, doi: 10.1016/j.akcej.2016.06.012
A. Khaksari and M. Ghorbani, “On the forgotten topological index”, Iranian journal mathematical chemistry, vol. 8, no. 3, pp. 327338, 2017, doi: 10.22052/IJMC.2017.43481
M. H. Khalifeh, H. YousefiAzari, and A. R. Ashrafi, “The first and second Zagreb indices of some graph operations”, Discrete applied mathematics, vol. 157, no. 4, pp. 804–811, Feb. 2009, doi:10.1016/j.dam.2008.06.015
X. Li and J. Zheng, “A unified approach to the extremal trees for different indices”, MATCH communications in mathematical and in computer chemistry, vol. 54, no. 1, pp. 195208, 2005. [On line]. Available: https://bit.ly/328TIFQ
I. Ž. Milovanović, V. M. Ćirić, I. Z. Milentijević, and E. I. Milovanović, “On some spectral, vertex and edge degreebased graph invariants”, MATCH communications in mathematical and in computer chemistry, vol. 77, no. 1, pp. 177188, 2017. [On line]. Available: https://bit.ly/3gIxKO3
N. De, S. M. A. Nayeem, and A. Pal, “Findex of some graph operations”, Discrete mathematics, algorithms and applications, vol. 8, no. 2, Art. ID. 1650025, 2016, doi: 10.1142/S1793830916500257
N. De, S. M. A. Nayeem, and A. Pal, “The Fcoindex of some graph operations”, SpringerPlus, vol. 5, no. 1, Art. ID. 221, Feb. 2016, doi: 10.1186/s4006401618647
P. S. Ranjini, V. Lokesha, and A. Usha, “Relation between phenylene and hexagonal squeeze using harmonic index”, International journal of graph theory, vol. 1, no. 4, pp. 116121, 2013
D. Sarala, H. Deng, S. K. Ayyaswamy, and B. Selvaraj, “The Zagreb indices of graphs based on four new operations related to the lexicographic product”, Applied mathematics and computation, vol. 309, pp. 156169, Sep. 2017, doi: 10.1016/j.amc.2017.04.002
P. Sarkar, N. De, and A. Pal, “The Zagreb indices of graphs based on new operations related to the join of graphs”, Journal of the international mathematical virtual institute, vol. 7, pp. 181209, 2017. [On line]. Available: https://bit.ly/3ef8rBJ
G. H. Shirdel, H. Rezapour and A. M. Sayadi, “The hyper Zagreb index of graph operations”, Iranian journal mathematical chemistry, vol. 4, no. 2, pp. 213220, 2013, doi: 10.22052/IJMC.2013.5294
Y. C. Sun, Z. Lin, W. X. Peng, T. Q. Yuan, F. Xu, Y. Q. Wu, J. Yang, Y. S. Wang and R. C. Sun, “Chemical changes of raw materials and manufactured binderless boards during hot pressing: lignin isolation and characterization”, Bioresources, vol. 9, no. 1, pp. 10551071, 2014, doi: 10.15376/biores.9.1.10551071
D. C. West, Introduction to graph theory, 2nd ed. India: Prentice Hall, 2008.
B. Zhou and I. Gutman, “Further properties of Zagreb indices”, MATCH communications in mathematical and in computer chemistry, vol. 54, no. 1, pp. 233239, 2005. [On line]. Available: https://bit.ly/3iMB6Sa
Published
How to Cite
Issue
Section
Copyright (c) 2020 A. Bharali, Amitav Doley, Jibonjyoti Buragohain
This work is licensed under a Creative Commons Attribution 4.0 International License.

Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
 No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.