On the inverse problem of some bond additive indices

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Document Type : Original paper

Authors

1 Department of Mathematics, Bishop Chulaparambil Memorial(B.C.M) College, Kottayam - 686001, Kerala, India

2 Department of Mathematics, St. Aloysius College, Edathua, Alappuzha-689573, India

3 Department of Mathematics, St. Stephens College, Uzhavoor-686634, Kerala, India

Abstract

Inverse Problem of topological indices deals with establishing whether or not a given number is a topological index of some graph. In this paper, we study the inverse topological index problem of some bond additive indices. In [1], it was conjectured that every positive integer except finitely many can be the Mostar index and edge Mostar index of some $c-$cyclic graph. We solve this conjecture for tricyclic graphs. We also study the inverse Albertson index problem and inverse sigma index problem for cacti and for cyclic graphs.

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References

[1] L. Alex and I. Gopalapillai, Inverse Mostar index problem for Chemical trees and Unicyclic graphs, Palest. J. Math., In Press.
[2] L. Alex and I. Gopalapillai, On a conjecture on edge mostar index of bicyclic graphs, Iranian J. Math. Chem. 14 (2023), no. 2, 97–108.  https://10.22052/IJMC.2023.248632.1680
[3] L. Alex and I. Gutman, On the inverse Mostar index problem for molecular graphs, Trans. Comb. In press.
[4] Rangaswami Balakrishnan and Kanna Ranganathan, A textbook of graph theory, Springer Science & Business Media, 2012.
[5] D. Dimitrov and D. Stevanović, On the σt-irregularity and the inverse irregularity problem, Appl. Math. Comput. 441 (2023), Article ID: 127709.  https://doi.org/10.1016/j.amc.2022.127709
[6] T. Došlić, I. Martinjak, R.Škrekovski, S.T. Spužević, and I. Zubac, Mostar index, J. Math. Chem. 56 (2018), no. 10, 2995–3013  https://doi.org/10.1007/s10910-018-0928-z
[7] I. Gutman, M. Togan, A. Yurttas, A.S. Cevik, and I.N. Cangul, Inverse problem for sigma index, MATCH Commun. Math. Comput. Chem 79 (2018), no. 2, 491–508.
[8] D.B. West, Introduction to Graph Theory, Prentice hall Upper Saddle River, 2001. 
[9] AYSUN Yurtta¸s Güne¸s, Müge Togan, Musa Demirci, and ˙ISMA˙IL Cangül, Inverse problem for Albertson irregularity index, Turk. World Math. Soc. J. Appl. Eng. Math. 12 (2022), no. 3, 808–815.
Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 03 August 2024

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