Maximal first Zagreb index of trees with given Roman domination number, By Doost Ali Mojdeh

Research

Title	Maximal first Zagreb index of trees with given Roman domination number
Type	Article
Keywords	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)

Abstract

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.