Minimizing and Computing the Inverse Geodesic Length on Trees

  title={Minimizing and Computing the Inverse Geodesic Length on Trees},
  author={Serge Gaspers and Joshua Lau},
The inverse geodesic length (IGL) of a graph $G=(V,E)$ is the sum of inverse distances between every two vertices: $IGL(G) = \sum_{\{u,v\} \subseteq V} \frac{1}{d_G(u,v)}$. In the MinIGL problem, the input is a graph $G$, an integer $k$, and a target inverse geodesic length $T$, and the question is whether there are $k$ vertices whose deletion decreases the IGL of $G$ to at most $T$. Aziz et al. (2018) proved that MinIGL is $W[1]$-hard for parameter treewidth, but the complexity status of the… 

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