A Mechanical Analysis of the Cyclic Structure of Undirected Linear Graphs

Abstract

A method of finding every cycle of an undirected linear graph by computation, rather than search, is presented. The method consists of three algorithms. The first produces a fundamental set of cycles from which all others can be generated. The second groups these cycles according to the nonseparable subgraphs of the original graph, and produces an ordering among groups that satisfies a condition required for the third algorithm. The third algorithm generates all and only cycles of the graph, without duplicates.