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

Abstract

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 the type matrix of S , which provides a classification of the way pairs of points are joined in S . Such a classification yields a criterion for colorability and unique colorability.