关键词: 色多项式, 伴随多项式, 色唯一, 伴随唯一

Abstract: Two graphs are chromatically equivalent if they have the same chromatic polynomials. A graph is said to be chromatically unique if each graph which has same chromatic polynomial is isomorphic with it. Similarly, two graphs are adjointly equivalent if they have the same adjoint polynomials. A graph is said to be adjointly unique if each graph which has same adjoint polynomial is isomorphic with it. As we all know, two graphs are chromatically equivalent if their complement are adjointly equivalent; a graph is chromatically unique if its complement is adjointly unique. In this paper, a necessary and sufficient condition of a classe graphs adjointly unique is given, thus a necessary and sufficient condition of their complement chromatically unique is given.

Key words: chromatic polynomial, adjoint polynomial, chromatic uniquness