Abstract:
A broadcast domination is a structure that combines classical domination and broadcasting formation. In order to design a broadcast scheme with limited capacity, the concept of k-limited broadcast domination is of interest. In this work, we show that a grid graph of dimension nxm can have a 3-limited broadcast with only one broadcast vertex if and only if \lfloor{\frac{n}{2}}\rfloor + \lfloor{\frac{m}{2}}\rfloor \leq k. In addition, we provide its upper bound for 3-limited broadcast domination number.