Skip to main content

The Forgotten Topological Index of Graphs Based on New Operations Related to the Join of Graphs

  • Conference paper
  • First Online:
Harmony Search and Nature Inspired Optimization Algorithms

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 741))

  • 1700 Accesses

Abstract

The sum of degree cube of all the vertices of a graph is known as the F-index or the “forgotten topological index” of that graph. In the present work, we study the “forgotten topological index” of new operations of different subdivision-related graphs based on the join of graphs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Gutman, I., Trinajestić, N.: Graph theory and molecular orbitals total \(\pi \)-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972)

    Article  Google Scholar 

  2. Sarkar, P., De, N., Pal, A.: The Zagreb Indices of graphs based on new operations related to the join of graphs. J. Int. Math. Virtual Inst. 7, 181–209 (2017)

    MathSciNet  Google Scholar 

  3. Mary, U., Arockiaraj, P.S., Albert, A.J.: The first and second Zagreb indices of corona graphs. Int. J. Math. Archive 5(11), 80–89 (2014)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. De, N.: F-index of graphs based on four operations related to the lexicographic product, arXiv:1706.00464v1

  6. De, N.: F-index and coindex of some derived graphs. Bull. Int. Math. Virtual Inst. 8, 81–88 (2018)

    MathSciNet  Google Scholar 

  7. De, N.: F-index of total transformation graphs. Discrete Math. Algorithm. Appl. 9(3) (2017)

    Google Scholar 

  8. Shirrdel, G.H., Rezapour, H., Sayadi, A.M.: The hyper Zagreb index of graph operations. Iran. J. Math. Chem. 4, 213–220 (2013)

    MATH  Google Scholar 

  9. De, N.: Hyper Zagreb index of bridge and chain graphs, arXiv:1703.08325v1

  10. Gao, W., Jamil, M.K., Farahani, M.R.: The hyper-Zagreb index and some graph operations. J. Appl. Math. Comput. 54, 263–275 (2017)

    Article  MathSciNet  Google Scholar 

  11. Kumar, R.P., Nandappa, D.S., Kanna, M.R.R.: Redefined Zagreb, randic, harmonic and GA indices of graphene. Int. J. Math. Anal. 11, 493–502 (2017)

    Article  Google Scholar 

  12. Farahani, M.R., Gao, W.: On multiplicative and redefined version of Zagreb indices of V-phenylenic nanotubes and nanotorus. British J. Math. Comput. Sci. 13(5), 1–8 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nilanjan De .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sarkar, P., De, N., Pal, A. (2019). The Forgotten Topological Index of Graphs Based on New Operations Related to the Join of Graphs. In: Yadav, N., Yadav, A., Bansal, J., Deep, K., Kim, J. (eds) Harmony Search and Nature Inspired Optimization Algorithms. Advances in Intelligent Systems and Computing, vol 741. Springer, Singapore. https://doi.org/10.1007/978-981-13-0761-4_33

Download citation

Publish with us

Policies and ethics