A note on a matrix criterion for unique colorability of a signed graph

A signed graph,S, is colorable if its point set can be partitioned into subsets such that all positive lines join points of the same subset and all negative lines join points of different subsets.S is uniquely colorable if there is only one such partition. Developed in this note is a new matrix, called thetype matrix ofS, which provides a classification of the way pairs of points are joined inS. Such a classification yields a criterion for colorability and unique colorability.The work reported here was supported by Grant MH 10834 from the National Institute of Mental Health.