| Abstract: | This paper investigates a conjecture of Lowell regarding the number of neighbors on maps divided into regions. Lowell speculated that border regions have on average three neighbors and that nonborder regions have on average six neighbors. This paper investigates the conjecture and, for a large category of maps, an exact relationship is obtained. Exceptions to this large category are considered, and a further exact relationship is obtained. The results of this paper may find applications not only for geographic maps, but also for models involving planar networks. |
