AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (234.3 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Maximal first Zagreb index of trees with given Roman domination number

Zhibin Du1, Ayu Ameliatul Shahilah Ahmad Jamri2( ), Roslan Hasni2, Doost Ali Mojdeh3
School of Software, South China Normal University, Foshan, Guangdong, China
Special Interest Group on Modeling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
Show Author Information

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.

Keywords

the first Zagreb indexdomination numberRoman domination number
CLC number: 05C78, 05C05, 05C07, 05C35

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 11801-11812
DOI: 10.3934/math.2022658

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Du Z, Jamri AASA, Hasni R, et al. Maximal first Zagreb index of trees with given Roman domination number. AIMS Mathematics, 2022, 7(7): 11801-11812. https://doi.org/10.3934/math.2022658

6

Views

1

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 25 November 2021
Revised: 27 December 2021
Accepted: 14 January 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)