Maximum second Zagreb index of trees with given Roman domination number

نویسندگان
Ahmad Jamri, Ayu Ameliatul Shahilah ID 1
Hasni, Roslan ID 2
Kamran Jamil, Muhammad ID 3
Mojdeh, Doost Ali ID 4

1 Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

2 Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

3 Department of Mathematics, Riphah International University, Lahore, Pakistan

4 Department of Mathematics, University of Mazandran, Babolsar, Iran

doi
10.22108/toc.2022.128323.1848
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