| Abstract |
For a vertex
v
in a simple, finite and undirected graph
G
=
(
V
(
G
)
,
E
(
G
)
)
, the neighborhood
N
G
(
v
)
of
v
is the set consisting of all vertices of
G
which are adjacent to
v
. A perfect Italian dominating function on
G
is a function
f
:
V
(
G
)
鈫�
{
0
,
1
,
2
}
such that for each
u
鈭�
V
(
G
)
with
f
(
u
)
=
0
,
鈭�
x
鈭�
N
G
(
u
)
f
(
x
)
=
2
. The weight of a perfect Italian dominating function
f
is the value
蠅
G
(
f
)
=
鈭�
v
鈭�
V
(
G
)
f
(
v
)
. The perfect Italian domination number of
G
is the minimum weight of a perfect Italian dominating function on
G
. In this paper, we study the perfect Italian domination in graphs under some binary operations. |
Mindanao State
University - Iligan Institute of Technology