Maximal first Zagreb index of trees with given Roman domination number

Zhibin Du; Ayu Ameliatul Shahilah Ahmad Jamri; Roslan Hasni; Doost Ali Mojdeh; Zhibin Du; Ayu Ameliatul Shahilah Ahmad Jamri; Roslan Hasni; Doost Ali Mojdeh

doi:10.3934/math.2022658

AIMS Mathematics

2022, Volume 7, Issue 7: 11801-11812. doi: 10.3934/math.2022658

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Research article

Maximal first Zagreb index of trees with given Roman domination number

Zhibin Du ¹,
Ayu Ameliatul Shahilah Ahmad Jamri ^{2
,
,},
Roslan Hasni ²,
Doost Ali Mojdeh ³

1.
School of Software, South China Normal University, Foshan, Guangdong, China
2.
Special Interest Group on Modeling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia
3.
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Received: 25 November 2021 Revised: 27 December 2021 Accepted: 14 January 2022 Published: 18 April 2022
MSC : 05C78, 05C05, 05C07, 05C35

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.
- the first Zagreb index,
- domination number,
- Roman domination number
Citation: Zhibin Du, Ayu Ameliatul Shahilah Ahmad Jamri, Roslan Hasni, Doost Ali Mojdeh. Maximal first Zagreb index of trees with given Roman domination number[J]. AIMS Mathematics, 2022, 7(7): 11801-11812. doi: 10.3934/math.2022658

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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.

References

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