Broadcast Domination of Triangular Matchstick Graphs and the Triangular Lattice
Pamela E. Harris, Dalia K. Luque, Claudia Reyes Flores, Nohemi Sepulveda · arXiv (Cornell University) · 2018
Blessing, Insko, Johnson and Mauretour gave a generalization of the domination number of a graph $G=(V,E)$ called the $(t,r)$ broadcast domination number which depends on the positive integer parameters $t$ and $r$. In this setting, a vertex $v \in V$ is a broadcast vertex of transmission strength $t$ if it transmits a signal of strength $t-d(u,v)$ to every vertex $u \in V$, where $d(u,v)$ denotes the distance between vertices $u$ and $v$ and $d(u,v)