Roman and Double Roman Domination Numbers for Wheel, Ladder, and Fan Graphs

Athraa Talib Breesam

doi:https://doi.org/10.14445/22315373/IJMTT-V72I6P103

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 6 | Year 2026 | Article Id. IJMTT-V72I6P103 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I6P103

Roman and Double Roman Domination Numbers for Wheel, Ladder, and Fan Graphs

Athraa Talib Breesam

Received	Revised	Accepted	Published
22 Apr 2026	28 May 2026	15 Jun 2026	29 Jun 2026

Citation :

Athraa Talib Breesam, "Roman and Double Roman Domination Numbers for Wheel, Ladder, and Fan Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 6, pp. 24-30, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I6P103

Abstract

We determine exact values of the Roman domination number γR(G) and the double Roman domination number γdR(G) for three foundational families of graphs: wheel graphs Wn (n ≥ 3), ladder graphs Ln (n ≥ 2), and fan graphs Fn (n ≥ 2). For wheel graphs, we establish γR(Wn) = 2 and γdR(Wn) = 3 for all n ≥ 3. For ladder graphs, we prove γR(Ln) = ⌈n/2⌉ + ⌈n/4⌉ and γdR(Ln) = 2⌈n/2⌉. For fan graphs, we show γR(Fn) = 2 and γdR(Fn) = 3 for all n ≥ 2. All six results are established through rigorous combinatorial proofs verified computationally for small cases. Graph diagrams illustrating optimal dominating functions accompany each result. Our analysis also reveals a quantitative separation in the γdR/γR ratio between centralized (wheel, fan) and distributed (ladder) graph families.

Keywords

Roman domination, Double Roman domination, Wheel graph, Ladder graph, Fan graph, Domination number, Graph theory.

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