Extremal trees with respect to the first and second reformulated Zagreb index

Downloads

DOI:

https://doi.org/10.26637/mjm503/006

Abstract

Let $G$ be a graph with edge set $E(G)$. The first and second reformulated Zagreb indices of $G$ are defined as $E M_1(G)=\sum_{e \in E(G)} \operatorname{deg}(e)^2$ and $E M_2(G)=\sum_{e \sim f} \operatorname{deg}(e) \operatorname{deg}(f)$,respectively, where $\operatorname{deg}(e)$ denotes the degree of the edge $e$, and $e \sim f$ means that the edges $e$ and $f$ are incident. In this paper, the extremal trees with respect to the first and second reformulated Zagreb indices are presented.

Keywords:

Tree, first reformulated Zagreb, second reformulated Zagreb, graph operation

Mathematics Subject Classification:

Mathematics
  • Ali Ghalavand Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317 − 51116, I. R. Iran.
  • Ali Reza Ashrafi Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317 − 51116, I. R. Iran.
  • Pages: 524-530
  • Date Published: 01-07-2017
  • Vol. 5 No. 03 (2017): Malaya Journal of Matematik (MJM)

N. De, Some bounds of reformulated Zagreb indices, Appl. Math. Sci. (Ruse), 6 (101-104) (2012), 5005-5012.

I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50 (2004), 83-92.

I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total $pi$-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17 (1972), 535-538. DOI: https://doi.org/10.1016/0009-2614(72)85099-1

A. Ilić and B. Zhou, On reformulated Zagreb indices, Discrete Appl. Math., 160 (3) (2012), 204-209. DOI: https://doi.org/10.1016/j.dam.2011.09.021

S. Ji, Y. Qu and X. Li, The reformulated Zagreb indices of tricyclic graphs, Appl. Math. Comput., 268 (2015), 590-595. DOI: https://doi.org/10.1016/j.amc.2015.06.058

S. Ji, X. Li and B. Huo, On reformulated Zagreb indices with respect to acyclic, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem., 72 (3)(2014), 723-732.

E. I. Milovanović, I. Ž. Milovanović, E. Ć. Dolićanin and E. Glogić, A note on the first reformulated Zagreb index, Appl. Math. Comput., 273 (2016), 16-20. DOI: https://doi.org/10.1016/j.amc.2015.09.088

A. Milićević, S. Nikolić and N. Trinajstić, On reformulated Zagreb indices, Mol. Divers., 8 (2004), 393-399. DOI: https://doi.org/10.1023/B:MODI.0000047504.14261.2a

S. Nikolić, G. Kovaćević, A. Milićević and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta., 76 (2003), 113-124.

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, 25(4) (2011), 75-83. DOI: https://doi.org/10.2298/FIL1104075S

B. Zhou and N. Trinajstić, Some properties of the reformulated Zagreb indices, J. Math. Chem., 48(3) (2010), 714-719. DOI: https://doi.org/10.1007/s10910-010-9704-4

B. Zhou and I. Gutman, Further properties of Zagreb indices, MATCH Commun. Math. Comput. Chem., 54 (2005), 233-239.

  • The research of the authors are partially supported by the University of Kashan under grant no 572760/3.

Metrics

PDF views
81
Jul 2017Jan 2018Jul 2018Jan 2019Jul 2019Jan 2020Jul 2020Jan 2021Jul 2021Jan 2022Jul 2022Jan 2023Jul 2023Jan 2024Jul 2024Jan 2025Jul 2025Jan 20269
|

Published

01-07-2017

How to Cite

Ali Ghalavand, and Ali Reza Ashrafi. “Extremal Trees With Respect to the First and Second Reformulated Zagreb Index”. Malaya Journal of Matematik, vol. 5, no. 03, July 2017, pp. 524-30, doi:10.26637/mjm503/006.

Issue

Vol. 5 No. 03 (2017): Malaya Journal of Matematik (MJM)

Section

Articles

License

Copyright (c) 2017 MJM

Creative Commons License

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

Crossref
Scopus
Google Scholar
Europe PMC