| Autor: |
Bozeman, Chassidy, Carlson, Joshua, Dairyko, Michael, Young, Derek, Young, Michael |
| Rok vydání: |
2018 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 $\frac{mn}{13.7619 + \epsilon(m,n)}$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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