A Note on Adjoint Polynomials and Uniquely Colorable Graphs

Haixing Zhao1, Ruying Liu 2
1Department of Computer Science and Engineering Northwestern Polytechnical University Xi’an, Shaanxi 710072, P. R. China
2Department of Mathematics, Qinghai Normal University Xining, Qinghai, 810008, P. R. China

Abstract

In this note, we present many uniquely \(n\)-colorable graphs with \(m\) vertices and new constructing ways of uniquely colorable graphs by using the theory of adjoint polynomials of graphs. We give new constructing ways of two uniquely colorable graphs which are chromatically equivalent also.