On 2k-Twisted Graphs

Abstract

We define the concept of a k -twisted chain in a (directed) graph and the concept of a 2 k -twisted graph. We show that for a 2 k -twisted graph the set of algebraic 2 k -twisted cycles is an integral spanning set for the integral flow module of G . Since a graph is 0-twisted if and only if it is strongly connected, our result generalizes the well-known theorem that there is a basis for the flow space of a strongly connected graph consisting of algebraic circuits.