Property And Application Of Chromatic Orbit Polynomials Of Graphs

The combinatorial counting and graph coloring is an important content of combinatorics and graph theory, The Polya’s Theory of counting and the chromatic polynomial are the main tools to study the above problems. In the literature [6], combining the Polya counting theorem and the chromatic polynomial together, Professor Du Qingyan introduced the notion of the chromatic orbit polynomial, and gives its expressions and its calculation methods. It provides the necessary tools and methods for counting problems of graph coloring under some action of groups. This thesis discusses some elementary properties and combination significance of chromatic orbit polynomial of graph, and corrects the chromatic orbit polynomial in a coloring of cube vertex coloring problem; The thesis also considers the simple accessories problem of necklaces, the main results involve pendants problem and inlaid problem of beads of necklaces; Finally, by the examples of the specific application in chemistry, it gives the appropriate instructions about the chromatic orbit polynomial.