A Linear Algorithm for the Cutting Center of a Tree

Abstract As a measure of the extent to which the removal of a node disconnects a graph, the cutting number c(v) of a node v in a connected graph G has been defined to be the number of pairs of nodes in different components of G−{v}. We present a linear algorithm for determining c(v) for all nodes of a tree, and hence for identifying the cutting center, which consists of the nodes v at which c(v) is maximized.