Let
be a connected
graph with vertex set
and edge set
.
We say a subset
of
dominates
if every vertex in
is adjacent to a vertex
in
. A generalization
of this concept is
broadcast domination. We designate certain vertices to be towers of signal strength
,
which send out signal to neighboring vertices with signal strength
decaying linearly as the signal traverses the edges of the graph. We let
be the set of all towers, and we define the signal received by a vertex
from all
towers
to
be
.
Blessing, Insko, Johnson and Mauretour defined a
broadcastdominating set, or a
broadcast, on
as a set
such
that
for all
. The minimum
cardinality of a
broadcast on
is called the
broadcast dominationnumber of
. We present
our research on the
broadcast domination number for certain graphs including paths, grid graphs, the
slant lattice, and the king’s lattice.
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