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Broadcasting is the process of message transmission in a communication network. The communication network is modeled by a graph \( G = (V, E) \), where the set of vertices \( V \) represents the network members and the set of edges \( E \) represents the communication links between two given vertices. We assume that \( G \) is connected and undirected. One vertex, called the \emph{originator} of the graph, holds a message that has to be transmitted to all vertices of the network by placing a series of calls over the network.
A \textbf{k-port} line broadcasting in \( G \) is a model in which an informed vertex can call, at each time unit, at most \( k \) vertices and transmit a message through a path, as long as two transmissions do not use the same edge at the same time. In case \( k \) is not bounded, the model is called the all-port line model.
In this paper, we extend Cohen’s work \([6]\), which handles the all-port line model.