Porous Exponential Domination in Harary Graphs

A porous exponential dominating set of a graph $G$ is a subset $S$ such that, for every vertex $v$ of $G$, $\sum_{u\in S}({1}/{2})^{d(u,v)-1}\geqslant 1$, where $ d(u,v) $ is the distance between vertices $ u $ and $ v $. The porous exponential domination number, $ \gamma_e^*(G) $, is the minimum cardinality of a porous exponential dominating set. In this paper, we determine porous exponential domination number of the Harary graph $ H_{k,n} $ for all $ k $ and $ n $.