Vol. 39, No. 2, 1971

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Matrix characterizations of circular-arc graphs

Alan Curtiss Tucker

Vol. 39 (1971), No. 2, 535–545

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 1’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 1’s property.

Mathematical Subject Classification 2000
Primary: 05C99
Received: 30 April 1970
Published: 1 November 1971
Alan Curtiss Tucker