The efficiency of AC graphs

Abstract

Given a graph G=( V, E), the problem of computing ε( G), the maximum efficiency of G, is that of computing the maximum number of nodes in V−R, over all sets R⊆ V, that are dominated by only one node in R. In “Efficient sets in graphs” by P.J. Bernhard a linear time algorithm that computes ε( G) when G is a tree is described. We show that a similar approach can be used to compute ε( G) when G is an AC graph.