Isomorphism of graph classes related to the circular-ones property

Abstract

We give a linear-time algorithm that checks for isomorphism between two 0 - 1 matrices that obey the circularones property. Our algorithm is similar to the isomorphism algorithm for interval graphs of Lueker and Booth, but works on PC trees, which are unrooted and have a cyclic nature, rather than with PQ trees, which are rooted. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, Γ circular-arc graphs, proper circular-arc graphs and convex-round graphs. © 2013 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.