The Adjoint Uniqueness Of Two Kinds Of Graphs

The studying of chromaticity problem of graphs is one of the important research area of graph theory.the chromatic polynomial of a graph is one of the main tools that is applied for studying the chromaticity of graphs.The graph G is adjoint uniqueness if and only if its complement G is chromatic uniqueness,then we can use the adjoint polynomials to investigate the chromaticity of a graph from the angle of its complement.In this paper,the adjoint uniqueness of two kinds of graphs is chiefly studied.In the first chapter,it mainly introduces the background of the paper and basic theoretical knowledge.In the second paper,devisible relation between the adjoint polynomials of the graphξ_n~3(2,1,n-6)and path P_n and sequence of the minmum adjoint real roots of some related graphs are first studied,then we obtain that the graphξ_n~3(2,1,n-6)(n≥7) is adjoint uniqueness if and only if n≠8,9,10 by use of these properties and character.In the third chapter,a necessary and sufficient condition of adjoint unique of the graphξ_n~3(3,1,n-7) is given by means of the properties of adjoint polynomials,including divisibility,minimum adjoint real roots,character and so on.