Maximum second Zagreb index of trees with given Roman domination number

Document Type : Research Paper


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 Department of Mathematics, Riphah International University, Lahore, Pakistan

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


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.


Main Subjects

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  • Receive Date: 24 April 2021
  • Revise Date: 11 January 2022
  • Accept Date: 29 January 2022
  • Published Online: 01 March 2023