Matrix characterrizations of circular-arc graphs

Abstract

A graph G is a circular-arc graph if there is a one-to-one correspondence between the vertices of G and a family of arcs on a circle such that two distinct vertices are adjacent when the corresponding arcs intersect. Circular-arc graphs are characterized as graphs whose adjacency matrix has the quasi-circular l’s property. Two interesting subclasses of circular-arc graphs are also discussed proper circular-arc graphs and graphs whose augmented adjacency matrix has the circular l’s property. © 1971 Pacific Journal of Mathematics.