On reformulated Narumi-Katayama index

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-05-0081

Keywords:

Degree, Graph, Graph operations, Reformulated NK-index, Topological indices

Abstract

A graph is a mathematical model form by set of dots for vertices some of which are connected by lines named as edges. A topological index is a numeric value obtained from a graph mathematically which characterize its topology. The reformulated Narumi-Katayama index of a graph G is defined as the product of edge degrees of all the vertices of G which is introduced in 1984, to used the carbon skeleton of a saturated hydrocarbons. The degree of an edge is given by the sum of degrees of the end vertices of the edge minus 2. In this paper, we compute the reformulated Narumi-Katayama index for different graph operations.

Author Biographies

Murat Cancan, Van Yüzüncü Yıl University.

Faculty of Education.

Nilanjan De, Calcutta Institute of Engineering and Management.

Dept. of Basic Sciences and Humanities (Mathematics)

Mehdi Alaeiyan, Iran University of Science and Technology.

Dept. of Mathematics

Mohammad Reza Farahani, Iran University of Science and Technology.

Dept. of Mathematics.

References

I. Gutman and N. Trinajsti?, “Graph theory and molecular orbitals. Total ?-electron energy of alternant hydrocarbons”, Chemical physics letters, vol. 17, no. 4, pp. 535–538, Dec. 1972, doi: 10.1016/0009-2614(72)85099-1

H. Narumi and M. Katayama, “Simple topological index: a newly devised index characterizing the topological nature of structural isomers of saturated hydrocarbons”, Memoirs of the Faculty of Engineering, Hokkaido University, vol. 16, no. 3, pp. 209-214, 1984. [On line]. Available: https://bit.ly/366Nzw7

Z. Tomovic and I. Gutman, “Narumi-Katayama index of phenylenes”, Journal of the Serbian Chemical Society, vol. 66, no. 4, pp. 243–247, 2001, doi: 10.2298/jsc0104243t

R. Todeschini, D. Ballabio, and V. Consonni, “Novel molecular descriptors based on functions of new vertex degrees”. En: I. Gutman and B. Furtula (Eds.), Novel molecular structure descriptors-theory and applications. Kragujevac: University Kragujevac, 2010, pp. 73–100.

M. Eliasi, A. Iranmanesh, and I. Gutman, “Multiplicative versions of first Zagreb index”, MATCH Communications in mathematical and in computer chemistry, vol. 68, no. 1, pp. 217-230, 2012. [On line]. Available: https://bit.ly/33UtOVO

R. Todeschini and V. Consonni, “New local vertex invariants and molecular descriptors based on functions of the vertex degrees”, MATCH Communications in mathematical and in computer chemistry, vol. 64, pp. 359–372, 2010. [On line]. Available: https://bit.ly/33YT4dA

I. Gutman, “Multiplicative Zagreb indices of trees”, Bulletin of international mathematical virtual institute, vol. 1, pp. 13-19, 2011. [On line]. Available: https://bit.ly/3j7hkjZ

K. Xu and H. Hua, “A unified approach to extremal multiplicative Zagreb indices for trees, unicyclic and bicyclic graphs”, MATCH Communications in mathematical and in computer chemistry, vol. 68, pp. 241–256, 2012. [On line]. Available: https://bit.ly/2HuhWCh

J. Liu and Q. Zhang, “Sharp upper bounds for multiplicative Zagreb Indices”, MATCH Communications in mathematical and in computer chemistry, vol. 68, pp. 231–240, 2012. [On line]. Available: https://bit.ly/2EzgJbT

S. Mondal, N. De, and A. Pal, “multiplicative degree based topological indices of nanostar dendrimers”, Biointerface research in applied chemistry, vol. 11, no. 1, pp. 7700–7711, Jul. 2021, doi: 10.33263/briac111.77007711

T. Réti and I. Gutman, “Relations between Ordinary and Multiplicative Zagreb Indices”, Bulletin of international mathematical virtual institute, vol. 2, pp. 133–140, 2012. [On line]. Available: https://bit.ly/3cwy8OK

A. Mili?evi?, S. Nikoli? and N. Trinajsti?, “On reformulated Zagreb indices”, Molecular diversity, vol. 8, no. 4, pp. 393–399, Dec. 2004, doi: 10.1023/B:MODI.0000047504.14261.2a

B. Zhou and N. Trinajsti?, “Some properties of the reformulated Zagreb indices”, Journal of mathematical chemistry, vol. 48, no. 3, pp. 714–719, Jun. 2010, doi: 10.1007/s10910-010-9704-4

A. Ili? and B. Zhou, “On reformulated Zagreb indices”, Discrete Applied Mathematics, vol. 160, no. 3, pp. 204–209, Feb. 2012, doi: 10.1016/j.dam.2011.09.021

G. Su, L. Xiong, L. Xu, and B. Ma, “On the maximum and minimum first reformulated Zagreb index of graphs with connectivity at most k”, Filomat, vol. 25, no. 4, pp. 75–83, 2011, doi: 10.2298/FIL1104075S

N. De, “Some bounds of reformulated Zagreb indices”, Applied mathematical sciences, vol. 6, no. 101, pp. 5505–5012, 2012. [On line]. Available: https://bit.ly/3cxWqrK

N. De, “Reformulated Zagreb indices of Dendrimers”, Mathematica aeterna, vol. 3, no. 2, pp. 133–138. [On line]. Available: https://bit.ly/3kPHAzP

S. Mondal, M. A. Ali, N. De, and A. Pal, “Bounds for neighborhood Zagreb index and its explicit expressions under some graph operations”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 799-819, Jul. 2020, doi: 10.22199/issn.0717-6279-2020-04-0050

M. Cancan, I. Ahmad, and S. Ahmad, “Molecular descriptors of certain OTIS interconnection networks”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 769-786, Jul. 2020, doi: 10.22199/issn.0717-6279-2020-04-0048

A. J. M. Khalaf, A. Javed, M. K. Jamil, M. Alaeiyan, and M. Reza Farahani, “Topological properties of four types of porphyrin dendrimers”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 979-993, Jul. 2020, doi: 10.22199/issn.0717-6279-2020-04-0061

Published

2020-10-01

How to Cite

[1]
M. . Cancan, N. De, M. Alaeiyan, and M. Reza Farahani, “On reformulated Narumi-Katayama index”, Proyecciones (Antofagasta, On line), vol. 39, no. 5, pp. 1333-1346, Oct. 2020.

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