TITLE:
On the Double Roman Domination in Spider Graphs
AUTHORS:
Wensheng Li, Zhongsheng Huang, Zhifang Feng
KEYWORDS:
Double Roman Dominating Function, Double Roman Domination Number, Spider Graphs
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.16 No.2,
April
22,
2026
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
v
for which
f(
v
)=0
has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex
v
for which
f(
v
)=1
has at least a neighbor labeled 2 or 3. The weight of a DRDF
f
is the value
w(
f
)=
∑
v∈V(
G
)
f(
v
)
. The minimum weight of a DRDF on a graph
G
is called the double Roman domination number of
G
. In this paper, we determine the exact value of the double Roman domination number of the Spider graphs
S
m,2
and
S
m,3
, and obtain an upper bound of the Spider graphs
S
m,n
.