On coherent configuration of circular-arc graphs

For any graph, Weisfeiler and Leman assigned the smallest matrix algebra which contains the adjacency matrix of the graph. The coherent configuration underlying this algebra for a graph Γ is called the coherent configuration of Γ, denoted by X(Γ). In this paper, we study the coherent configuration of circular-arc graphs. We give a characterization of the circular-arc graphs Γ, where X(Γ) is a homogeneous coherent configuration. Moreover, all homogeneous coherent configurations which are obtained in this way are characterized as a subclass of Schurian coherent configurations.