Some Bounds on \(a\)-Analogue Atom-Bond Connectivity Related Indices

Authors

DOI:

https://doi.org/10.26713/cma.v14i4.2482

Keywords:

ABC indices, a-analogue ABC indices

Abstract

For any non-real number \(a\), the significance of the \(a\)-analogue Atom-Bond Connectivity indices lies within the actuality of their particular cases for well-chosen values for the variant \(a\). In this paper, we obtained some bounds based on the vertex-degree along with the variant \(a\) value, inequalities in other degree-based indices, and characterizations of these novel \(a\)-analogue \(ABC\) indices.

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References

M. B. Ahmadi, D. Dimitrov, I. Gutman and S. A. Hosseini, Disproving a conjecture on trees with minimal atom-bond connectivity index, MATCH Communications in Mathematical and in Computer Chemistry 72(3) (2014), 685 – 698, URL: https://match.pmf.kg.ac.rs/electronic_versions/Match72/n3/match72n3_685-698.pdf.

F. E. Alsaadi, S. A. U. H. Bokhary, A. Shah, U. Ali, J. Cao, M. O. Alassafi, M. U. Rehman and J. U. Rahman, On knowledge discovery and representations of molecular structures using topological indices, Journal of Artificial Intelligence and Soft Computing Research 11(1) (2021), 21 – 32, DOI: 10.2478/jaiscr-2021-0002.

N. L. Carothers, Real Analysis, Cambridge University Press, Cambridge (2000), DOI: 10.1017/CBO9780511814228.

B. Chaluvaraju and A. B. Shaikh, Different versions of atom-bond connectivity indices of some molecular structures: applied for the treatment and prevention of COVID-19, Polycyclic Aromatic Compounds 42(6) (2022), 3748 – 3761, DOI: 10.1080/10406638.2021.1872655.

K. C. Das, Atom-bond connectivity index of graphs, Discrete Applied Mathematics 158(11) (2010), 1181 – 1188, DOI: 10.1016/j.dam.2010.03.006.

K. C. Das, I. Gutman and B. Furtula, On atom-bond connectivity index, Chemical Physics Letters 511(4-5) (2011), 452 – 454, DOI: 10.1016/j.cplett.2011.06.049.

K. C. Das, J. M. Rodríguez and J. M. Sigarreta, On the generalized ABC index of graphs, MATCH Communications in Mathematical and in Computer Chemistry 87(1) (2022), 147 – 169, DOI: 10.46793/match.87-1.147D.

D. Dimitrov, On structural properties of trees with minimal atom-bond connectivity index II: Bounds on B1- and B2-branches, Discrete Applied Mathematics 204 (2016), 90 – 116, DOI: 10.1016/j.dam.2015.10.010.

E. Estrada, Atom-bond connectivity and the energetic of branched alkanes, Chemical Physics Letters 463(4-5) (2008), 422 – 425, DOI: 10.1016/j.cplett.2008.08.074.

E. Estrada, L. Torres, L. Rodríguez and I. Gutman, An atom-bond connectivity index: modeling the enthalpy of formation of alkanes, Indian Journal of Chemistry 37A (1998), 849 – 855, URL: https://nopr.niscpr.res.in/bitstream/123456789/40308/1/IJCA%2037A%2810%29%20849-855.pdf.

G. B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd edition, John Wiley and Sons, 416 pages (1999), URL: https://www.wiley.com/en-us/Real+Analysis:+Modern+Techniques+and+Their+Applications,+2nd+Edition-p-9780471317166.

I. Gutman, Procena energija zasnovanih na stepenima cvorova, Vojnotehnicki Glasnik 70(1) (2022), 13 – 23, DOI: 10.5937/vojtehg70-35584.

I. Gutman and B. Furtula, Trees with smallest atom-bond connectivity index, MATCH Communications in Mathematical and in Computer Chemistry 68 (2012), 131 – 136, URL: https://match.pmf.kg.ac.rs/electronic_versions/Match68/n1/match68n1_131-136.pdf.

F. Harary, Graph Theory, Addison Wesley Publishing Company, Reading Massachusetts (1969), URL: https://users.metu.edu.tr/aldoks/341/Book%201%20(Harary).pdf.

V. R. Kulli, Graph indices, Chapter 3, in: Handbook of Research on Advanced Applications of Graph Theory in Modern Society, M. Pal, S. Samanta and A. Pal (editors), IGI Global, USA, pp. 66 – 91 (2019), DOI: 10.4018/978-1-5225-9380-5.

W. Lin, J. Chen, C. Ma, Y. Zhang, J. Chen, D. Zhang and F. Jia, On trees with minimal ABC index among trees with given number of leaves, MATCH Communications in Mathematical and in Computer Chemistry 76 (2016), 131 – 140, URL: https://match.pmf.kg.ac.rs/electronic_versions/Match76/n1/match76n1_131-140.pdf.

J. L. Palacios, A resistive upper bound for the ABC index, MATCH Communications in Mathematical and in Computer Chemistry 72 (2014), 709 – 713, URL: https://match.pmf.kg.ac.rs/electronic_versions/Match72/n3/match72n3_709-713.pdf.

B. Sarveshkumar, V. R. Kulli and B. Chaluvaraju, Some inequalities on generalized degree based indices: An (a,b)-KA indices and coindices, Proceedings of the Jangjeon Mathematical Society 26(1) (2023), 43 – 53, URL: https://jangjeonopen.or.kr/public/upload/1675228591-pjms26-1-4.pdf.

R. Zheng, Bounds on the general atom-bond connectivity indices, MATCH Communications in Mathematical and in Computer Chemistry 83 (2020), 143 – 166, URL: https://match.pmf.kg.ac.rs/electronic_versions/Match83/n1/match83n1_143-166.pdf.

B. Zhou and N. Trinajstic, On a novel connectivity index, Journal of Mathematical Chemistry 46 (2009), 1252 – 1270, DOI: 10.1007/s10910-008-9515-z.

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Published

25-12-2023
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How to Cite

Sarveshkumar, B., & Chaluvaraju, B. (2023). Some Bounds on \(a\)-Analogue Atom-Bond Connectivity Related Indices. Communications in Mathematics and Applications, 14(4), 1293–1300. https://doi.org/10.26713/cma.v14i4.2482

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Research Article