On exponential trees (Q1378292)

The paper considers locally finite graphs \(G=(V,E)\). \(G\) is called exponential if \(| G^d(X) |>2 \cdot | X|\) holds for an integer \(d\) and for every finite subset \(X\) of \(V\), where \(G^d(X)\) is the set of all vertices of \(G\) whose distance to a vertex in \(X\) is at most \(d\). The paper gives a characterization of exponentiality for a large class of trees.