Consider a broadcast scheme on a connected graph from an originator vertex in a graph
consisting of a sequence of parallel calls starting from
. In each time step, every informed node
(sender) can call at most one uninformed neighbor (receiver), corresponding to a
directed edge. The process is iterated until every vertex in the network is informed,
with the result being a directed spanning tree of
rooted at
called the broadcast tree of originator
.
The minimum number of time steps required to broadcast from to all vertices in the graph
is called the broadcast time of vertex
, denoted
. The maximum broadcast time over all originator vertices
in
is called the broadcast time of
, denoted
(Harutyunyan1 and Li 2019).
The broadcast time of a disconnected graph is the maximum of the broadcast times of its connected components.