Research Article
The Double Roman Domination Number of Sunlet Graphs Sn
Wensheng Li*
Issue:
Volume 15, Issue 4, August 2026
Pages:
73-78
Received:
21 September 2026
Accepted:
4 October 2026
Published:
21 October 2026
DOI:
10.11648/j.pamj.20261504.12
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Abstract: A double Roman dominating function (DRDF) f on a given graph G is a mapping from V(G) to {0, 1, 2, 3} in such a way that a vertex u for which f(u) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex u for which f(u) = 1 has at least a neighbor labeled 2 or 3. The weight of a DRDF f is the value w(f) = ∑u∈V(G) f(u). The minimum weight of a DRDF on a graph G is called the double Roman domination number γdR(G) of G. A Sunlet graph Sn is constructed from an n-cycle by attaching one pendant vertex to each vertex of the cycle. This paper investigates the double Roman domination of Sunlet graphs Sn for integer n≥3. Using three lemmas, we derive the exact formula γdR(Sn)=⌈7n/3⌉. We further analyze whether Sunlet graphs belong to the family of double Roman graphs. By comparing the domination number γ(Sn)=n with the known inequality 2γ(G)≤γdR(G)≤3γ(G) for double Roman graphs, we prove that Sn fails to satisfy the required inequality, which implies no Sunlet graph is a double Roman graph. The obtained result gives an explicit expression for the double Roman domination number of this class of unicyclic graphs and enriches the research achievements of double Roman domination theory for unicyclic graphs.
Abstract: A double Roman dominating function (DRDF) f on a given graph G is a mapping from V(G) to {0, 1, 2, 3} in such a way that a vertex u for which f(u) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex u for which f(u) = 1 has at least a neighbor labeled 2 or 3. The weight of a DRDF f is the value w(f) = ∑u∈V(G) f(u). Th...
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