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.