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Maximum second Zagreb index of trees with given Roman domination number | ||
| Transactions on Combinatorics | ||
| مقاله 9، دوره 12، شماره 1، خرداد 2023، صفحه 1-10 اصل مقاله (418.19 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.128323.1848 | ||
| نویسندگان | ||
| Ayu Ameliatul Shahilah Ahmad Jamri1؛ Roslan Hasni* 1؛ Muhammad Kamran Jamil2؛ Doost Ali Mojdeh3 | ||
| 1Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia | ||
| 2Department of Mathematics, Riphah International University, Lahore, Pakistan | ||
| 3Department of Mathematics, University of Mazandran, Babolsar, Iran | ||
| چکیده | ||
| Chemical study regarding total $\pi$-electron energy with respect to conjugated molecules has focused on the second Zagreb index of graphs. Moreover, in the last half-century, it has gotten a lot of attention. The relationship between the Roman domination number and the second Zagreb index is investigated in this study. We characterize the trees with the maximum second Zagreb index among those with the given Roman domination number. | ||
| کلیدواژه‌ها | ||
| The second Zagreb index؛ Domination number؛ Roman domination number | ||
| مراجع | ||
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[1] A. Alhashim, W. J. Desormeaux and T. W. Haynes, Roman domination in complementary prisms, Australas. J. Combin., 68 (2017) 218–228. [2] B. Borovi´canin and B. Furtula, On extremal Zagreb indices of trees with given domination number, Appl. Math. Comput., 279 (2016) 208–218. [3] B. Borovi´canin, K. C. Das, B. Furtula and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem., 78 (2017) 17–100. [4] D. A. Mojdeh, A. Parsian and I. Masoumi, Strong Roman domination number in complementary prism graphs, Turk. J. Math. Comput. Sci., 11 (2019) 40–47. [5] D. A. Mojdeh, M. Habibi, L. Badakdshian and Y. S. Rao, Zagreb indices of trees, unicyclic and bicyclic graphs with given (total) domination, IEEE Access, 7 (2019) 94143–94149. [6] D. B. West, Introduction to Graph Theory, 2nd Edition, Prentice Hall, NJ, 2001. [7] D. Stevanovi´c, Mathematical properties of Zagreb indices, Akademska Misan, Belgrade (in Serbian), 2014. [8] E. J. Cockayne, P. A. Dreyer, S. M. Hedetniemi and S. T. Hedetniemi, Roman domination in graphs, Discrete Maths., 278 (2004) 11–22. [9] E. J. Cockayne, R. M. Dawes and S. T. Hedetniemi, Total domination in graphs, Networks, 10 (1980) 211–219. [10] I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., 50 (2004) 83–92. [11] I. Gutman and N. Trinajsti´c, Graph theory and molecular orbitals. Total ϕ- electron energy of alternant hydrocarbons, Chem. Phsy. Lett., 17 (1972) 535–538. http://dx.doi.org/10.22108/TOC.2022.128323.1848 10 Trans. Comb. 12 no. 1 (2023) 1-10 A. A. S. Ahmad Jamri, R. Hasni, M. K. Jamil and D. A. Mojdeh [12] J. Amjadi, R. Khoeilar, M. Chellali and Z. Shao’, On the Roman domination subdivision number of a graph, J. Comb. Optim., 40 (2020) 501–511. [13] K. Xu, The Zagreb indices of graphs with a given clique number, Appl. Math. Lett., 24 (2011) 1026–1030. [14] M. A. Henning, A characterization of Roman trees, Discuss. Math. Graph Theory, 22 (2002) 325–334. [15] O. Favaron, H. Karami, R. Khoeilar and S. M. Sheikholeslami, On the Roman domination number of a graph, Discrete Math., 309 (2009) 3447–3451. [16] P. Dankelmann, Average distance and domination number, Discrete Appl. Math., 80 (1997) 21–35. [17] R. Todeschini and V. Consonni, Handbook of molecular descriptors, Wiley-VCH, Weinheim, 2000. [18] S. Bermudo, J. E. N´apoles and J. Rada, Extremal trees for the Randi´c index with given domination number, Appl. Math. Comput., 375 (2020). [19] S. Nikoli´c, G. Kova´cevi´c, A. Mili´cevi´c and N. Trinajsti´c, The Zagreb indices 30 years after, Croat. Chem. Acta, 76 (2003) 113–124. [20] T. Dehghan-Zadeh, H. Hua, A. R. Ashrafi and N. Habibi, Extremal tricyclic graphs with respect to the first and second Zagreb indices, Note Mat., 33 (2013) 107–121. [21] W. G. Yuan and X. D. Zhang, The second Zagreb indices of graphs with given degree sequences, Discrete Appl. Math., 185 (2015) 230–238. [22] Z. Du, A. A. S. Ahmad Jamri, R. Hasni and D. A. Mojdeh, Maximal first Zagreb index of trees with given Roman domination number, AIMS Maths., accepted for publication. [23] Z. Yan, H. Liu and H. Liu, Sharp bounds for the second Zagreb index of unicyclic graphs, J. Math. Chem., 42 (2007) 565–574. | ||
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