Roman Domination of Cartesian Bundles of Cycles over Cycles

Simon Brezovnik () and Janez Žerovnik
Additional contact information
Simon Brezovnik: Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia
Janez Žerovnik: Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia

Mathematics, 2025, vol. 13, issue 15, 1-18

Abstract: A Roman dominating function f of a graph G = ( V , E ) assigns labels from the set { 0 , 1 , 2 } to vertices such that every vertex labeled 0 has a neighbor labeled 2. The weight of an RDF f is defined as w ( f ) = ∑ v ∈ V f ( v ) , and the Roman domination number, γ R ( G ) , is the minimum weight among all RDFs of G . This paper studies the domination and Roman domination numbers in Cartesian bundles of cycles. Furthermore, the constructed optimal patterns improve known bounds and suggest even better bounds might be achieved by combining patterns, especially for bundles involving shifts of order 4 k and 5 k .

Keywords: Roman domination; domination; graph bundles; Roman graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/15/2351/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/15/2351/ (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:13:y:2025:i:15:p:2351-:d:1708086

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 ().