Abstract
The first reformulated Zagreb index of trees can take any even positive integer greater than 8, whereas the second reformulated Zagreb index of trees can take all positive integers greater than 47 with a few exceptional values less than 8 and 47, respectively. The entire Zagreb index is defined in terms of edge degrees and incorporates the idea of intermolecular forces between atoms along with atoms and bonds. This intricate significance of studying the entire Zagreb index led to the generalization of the first entire Zagreb index of trees. The inverse problem on the first entire Zagreb of trees gives the existence of a tree for any even positive integer greater than 46.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Harry W (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69(1):17–20
Sonja N, Goran K, Ante M, Nenad T (2003) The Zagreb indices 30 years after. Croatica Chem Acta 76(2):113–124
Cao J, Ali U, Javaid M, Huang C (2020) Zagreb connection indices of molecular graphs based on operations. Complexity
Ante M, Sonja N, Nenad T (2004) On reformulated Zagreb indices. Molecular Diversity 8(4):393–399
Bo Z, Nenad T (2010) Some properties of the reformulated Zagreb indices. J Math Chem 48(3):714–719
Nilanjan D (2012) Some bounds of reformulated Zagreb indices. Appl Math Sci 6(101):5005–5012
Shengjin J, Xia L, Bofeng H (2014) On reformulated Zagreb indices with respect to acyclic, unicyclic and bicyclic graphs. MATCH Commun Math Comput Chem 72(3):723–732
Milovanović EI, Milovanović IŽ, Dolićanin EĆ, Glogić E (2016) A note on the first reformulated zagreb index. Appl Math Comput 273:16–20
Qu T, Mengya H, Shengjin J, Xia L (2020) Note on the reformulated Zagreb indices of two classes of graphs. J Chem 1–4:2020
Nilanjan D (2013) Reformulated Zagreb indices of dendrimers. Math Aeterna 3(2):133–138
Husin MN, Hasni R, Imran M (2017) More results on computation of topological indices of certain networks. Int J Network Virt Org 17(1):46–63
Liu J-B, Ali B, Malik MA, Afzal Siddiqui HM, Imran M (2019) Reformulated Zagreb indices of some derived graphs. Mathematics 7(4):366
Alwardi A, Alqesmah A, Rangarajan R, Cangul IN (2018) Entire Zagreb indices of graphs. Discrete Math Alg Appl 10(03):1850037
Luo L, Dehgardi N, Fahad A (2020) Lower bounds on the entire zagreb indices of trees. Discrete Dynam Nat Soc
Ghalavand A, Reza Ashrafi A (2019) Bounds on the entire Zagreb indices of graphs. MATCH Commun Math Comput Chem 81:371–381
Yurtas A, Togan M, Lokesha V, Cangul IN, Gutman I (2019) Inverse problem for Zagreb indices. J Math Chem 57(2):609–615
Gutman I, Trinajstić N (1972) Graph theory and molecular orbitals. Total \(\varphi \)-electron energy of alternant hydrocarbons. Chemical Phys Lett 17(4):535–538
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Asok, A., Kureethara, J.V. (2024). Extremal Trees of the Reformulated and the Entire Zagreb Indices. In: Sharma, H., Chakravorty, A., Hussain, S., Kumari, R. (eds) Artificial Intelligence: Theory and Applications. AITA 2023. Lecture Notes in Networks and Systems, vol 844. Springer, Singapore. https://doi.org/10.1007/978-981-99-8479-4_29
Download citation
DOI: https://doi.org/10.1007/978-981-99-8479-4_29
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-8478-7
Online ISBN: 978-981-99-8479-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)