Maximal first Zagreb index of trees with given Roman domination number

AIMS Mathematics

article

Zhibin Du¹  Ayu Ameliatul Shahilah Ahmad Jamri²  Roslan Hasni²  Doost Ali Mojdeh³ 

[1] School of Software, South China Normal University;Special Interest Group on Modeling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu;Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran

关键词: the first Zagreb index;    domination number;    Roman domination number;   

DOI  :  10.3934/math.2022658

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY