Feedback Vertex Sets in Rotator Graphs

Abstract

This paper provides an algorithm for finding feedback vertex set in rotator graphs. Feedback vertex set is a subset of a graph whose removal causes an acyclic graph and is developed in various topologies of interconnected networks. In 1992, Corbett pioneered rotator graphs, whose interesting topological structures attract many researchers to publish relative papers in recent years. In this paper, we first develops feedback vertex set algorithm for rotator graphs. Our algorithm utilizes the technique of dynamic programming and generates a feedback vertex set of size n!/3 for a rotator graph of scale n, which contains n! nodes. The generated set size is proved to be minimum. Finding a minimum feedback vertex set is a NP-hard problem for general graphs. The time complexity of our algorithm, which finds a minimum feedback vertex set for a rotator graph of scale n, is proved to be O(nn−−3).