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Extremal Zagreb indices of a tree with given double Roman domination number | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 شهریور 1404 اصل مقاله (419.84 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30411.2456 | ||
| نویسندگان | ||
| Mohammad Habibi* ؛ Amene Alidadi | ||
| Department of Mathematics, Tafresh University, Tafresh 39518-79611, Iran | ||
| چکیده | ||
| In this article, some upper and lower bounds for the first and the second Zagreb indices of an arbitrary tree in terms of its order and double Roman domination number $\gamma_{dR}$, (depending on whether $\gamma_{dR}$ is odd or even), are stated. Also, all extremal trees attaining equality are characterized. | ||
| کلیدواژهها | ||
| Double Roman domination number؛ double star؛ path؛ tree؛ Zagreb indices | ||
| مراجع | ||
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[2] A.A.S. Ahmad Jamri, R. Hasni, M. Kamran Jamil, and D.A. Mojdeh, Maximum second Zagreb index of trees with given Roman domination number, Trans. Comb. 12 (2023), no. 1, 1–10. https://doi.org/10.22108/toc.2022.128323.1848
[3] A.A.S. Ahmad Jamri, R. Hasni, and S.K. Said Husain, On the Zagreb indices of graphs with given Roman domination number, Commun. Comb. Optim. 8 (2023), no. 1, 141–152. https://doi.org/10.22049/cco.2021.27439.1263
[4] A.A.S. Ahmad Jamri, F. Movahedi, R. Hasni, and M.H. Akhbari, A lower bound for the second Zagreb index of trees with given Roman domination number, Commun. Comb. Cptim. 8 (2023), no. 2, 391–396. https://doi.org/10.22049/cco.2022.27553.1288
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