On the broadcast independence number of locally uniform 2-lobsters

Let~$G$ be a simple undirected graph. A broadcast on~$G$ is a function $f : V(G)\rightarrow\NNNNN$ such that $f(v)\le e_G(v)$ holds for every vertex~$v$ of~$G$, where $e_G(v)$ denotes the eccentricity of~$v$ in~$G$, is, maximum distance from~$v$ to any other vertex of~$G$. The cost of~$f$ is value $\cost(f)=\sum_{v\in V(G)}f(v)$. A broadcast~$f$ independent if two distinct vertices $u$ and~$v$ $d_G(u,v)>\max\{f(u),f(v)\}$, where $d_G(u,v)$ between in~$G$. The independence number of~$G$ then defined as of an on~$G$. A caterpillar tree that, after removal all leaf vertices, remaining graph non-empty path. A lobster caterpillar. In [M. Ahmane, I. Bouchemakh and E. Sopena. On Broadcast Independence Number Caterpillars. Discrete Applied Mathematics, in press (2018)], we studied broadcasts caterpillars. In this paper, carrying on with line research, consider lobsters and give explicit formula the broadcast family called locally uniform $2$-lobsters.