May 29, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences


Title Maximal first Zagreb index of trees with given Roman domination number
Type Article
the first Zagreb index, domination number, Roman domination number
Journal AIMS Mathematics
DOI 10.3934/math.2022658
Researchers Zhibin Du (First researcher) , A. A. Shahilah Ahmad Jamri (Second researcher) , Roslan Hasni (Third researcher) , Doost Ali Mojdeh (Fourth researcher)


The first Zagreb index of graphs is defined to be the sum of squares of degrees of all the vertices of graphs. It drew a great deal of attention in the past half-century. In this paper, we study the relationship between the first Zagreb index and Roman domination number of graphs. More precisely, we characterize the trees with the maximum first Zagreb index among trees with given Roman domination number.