On circular-arc graphs with association schemes

TL;DR

This paper characterizes circular-arc graphs with association schemes and proves that all such schemes are Schurian, providing a comprehensive understanding of their structure and classification.

Contribution

It offers a complete characterization of circular-arc graphs with association schemes and identifies that all these schemes are Schurian, advancing the theoretical understanding of their properties.

Findings

Characterization of circular-arc graphs with association schemes

All association schemes of these graphs are Schurian

Provides a classification framework for these graphs and schemes

Abstract

In this paper, we give a characterization of the class of all circular-arc graphs whose schemes are association. Moreover, all association schemes which are the scheme of a circular-arc graph are characterized, specially it is proved that they are Schurian.