| Abstract |
Let
be a connected graph. A function
is a double Roman dominating function of
if for each
with
,
has two adjacent vertices
and
for which
or
has an adjacent vertex
for which
, and for each
with
,
is adjacent to a vertex
for which either
or
. The minimum weight
of a double Roman dominating function
of
is the double Roman domination number of
. In this paper, we continue the study of double Roman domination introduced and studied by R.A. Beeler et al. in [2]. First, we characterize some double Roman domination numbers with small values in terms of the domination numbers and 2-domination numbers. Then we determine the double Roman domination numbers of the join, corona, complementary prism and lexicographic product of graphs. |
Mindanao State
University - Iligan Institute of Technology