Roman domination of cartesian bundles of cycles over cycles

Brezovnik, Simon (author), Žerovnik, Janez (author)

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, yR(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 4k and 5k.

• Language: English
• Keywords: Roman domination, domination, graph bundles, Roman graphs
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 18 str.
• Numbering: Vol. 13, iss. 15, art. 2351
• PID: 20.500.12556/RUL-170980
• UDC: 519.17
• ISSN on article: 2227-7390
• DOI: 10.3390/math13152351
• COBISS.SI-ID: 243736579
• Publication date in RUL: 24.07.2025

Record is a part of a journal

• Title: Mathematics
• Shortened title: Mathematics
• Publisher: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

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• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
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