Dominating Broadcasts in Fuzzy Graphs

Passawan Noppakaew, Kaewkan Hengthonglert and Sawanya Sakuntasathien
Additional contact information
Passawan Noppakaew: Department of Mathematics, Faculty of Science, Silpakorn University, Bangkok 10200, Thailand
Kaewkan Hengthonglert: Department of Mathematics, Faculty of Science, Silpakorn University, Bangkok 10200, Thailand
Sawanya Sakuntasathien: Department of Mathematics, Faculty of Science, Silpakorn University, Bangkok 10200, Thailand

Mathematics, 2022, vol. 10, issue 2, 1-8

Abstract: Broadcasting problems in graph theory play a significant role in solving many complicated physical problems. However, in real life there are many vague situations that sometimes cannot be modeled using usual graphs. Consequently, the concept of a fuzzy graph G F : ( V , σ , μ ) has been introduced to deal with such problems. In this study, we are interested in defining the notion of dominating broadcasts in fuzzy graphs. We also show that, in a connected fuzzy graph containing more than one element in σ * , a dominating broadcast always exists, where σ * is { v ∈ V | σ ( v ) > 0 } . In addition, we investigate the relationship between broadcast domination numbers, radii, and domination numbers in a fuzzy graph as follows; γ b ( G F ) ≤ min { r ( G F ) , γ ( G F ) } , where γ b ( G F ) is the broadcast domination number, r ( G F ) is the radius, and γ ( G F ) is domination numbers in fuzzy graph G F , with | σ * | > 1 .

Keywords: dominating broadcast; broadcast domination number; domination number; fuzzy graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/2/281/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/2/281/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:2:p:281-:d:726770

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().