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تسجيل مستخدم جديدLower Bounds for the Exponential Domination Number of $C_m times C_n$
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A vertex $v$ in a porous exponential dominating set assigns weight $left(tfrac{1}{2}right)^{dist(v,u)}$ to vertex $u$. A porous exponential dominating set of a graph $G$ is a subset of $V(G)$ such that every vertex in $V(G)$ has been assigned a sum weight of at least 1. In this paper the porous exponential dominating number, denoted by $gamma_e^*(G)$, for the graph $G = C_m times C_n$ is discussed. Anderson et. al. proved that $frac{mn}{15.875}le gamma_e^*(C_m times C_n) le frac{mn}{13}$ and conjectured that $frac{mn}{13}$ is also the asymptotic lower bound. We use a linear programing approach to sharpen the lower bound to $frac{mn}{13.7619 + epsilon(m,n)}$.
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