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On the inverse problem of some bond additive indices | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 مرداد 1403 | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29470.2019 | ||
| نویسندگان | ||
| Liju Alex* 1؛ Indulal Gopalapillai2؛ John Joy Mulloor3 | ||
| 1Department of Mathematics, Bishop Chulaparambil Memorial(B.C.M) College, Kottayam - 686001, Kerala, India | ||
| 2Department of Mathematics, St. Aloysius College, Edathua, Alappuzha-689573, India | ||
| 3Department of Mathematics, St. Stephens College, Uzhavoor-686634, Kerala, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Inverse Problem؛ Mostar Index؛ Edge Mostar Index؛ Tricyclic Graph؛ Albertson Index | ||
| مراجع | ||
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[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. | ||
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