| Abstract |
Let
G
be a finite simple graph. A set
S
鈯�
V
(
G
)
is a total hop dominating set of
G
if for every
v
鈭�
V
(
G
)
, there exists
u
鈭�
S
such that
d
G
(
u
,
v
)
=
2
. Any total hop dominating set of
G
of minimum cardinality is a
纬
th
-set of
G
. A total hop dominating set
S
of
G
which intersects every
纬
th
-set of
G
is a transversal total hop dominating set. The minimum cardinality
藛
纬
th
(
G
)
of a transversal total hop dominating set in
G
is the transversal total hop domination number of
G
. In this paper, we initiate the study of transversal total hop domination in graphs. First, we characterize a graph
G
of order
n
for which
藛
纬
th
(
G
)
is
n
or
n
鈭�
1
, and also we determine the specific values of
藛
纬
th
(
G
)
for some special graphs
G
. Next, we solve some realization problems involving
藛
纬
th
(
G
)
with other parameters of
G
. Finally, we investigate the transversal total hop domination in the complementary prism, corona, and lexicographic product of graphs. |
Mindanao State
University - Iligan Institute of Technology