Open AccessMaximal first Zagreb index of trees with given Roman domination number
Author(s) -
Zhibin Du,
Ayu Ameliatul Shahilah Ahmad Jamri,
Roslan Hasni,
Doost Ali Mojdeh
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022658
Subject(s) - combinatorics , index (typography) , mathematics , domination analysis , tree (set theory) , graph , computer science , world wide web , vertex (graph theory)
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.