The dissimilarity characteristic theorem for k-supertrees and its application

Abstract

In the theory of graphical enumeration, the Pólya's theorem and the dissimilarity characteristic theorem for a class of graphs are two of the necessary conditions for enumeration of the graphs in the class. In this paper, we define k-supertrees and give a dissimilarity characteristic theorem for k-supertrees. We also provide the applications of this theorem to the traditional 2-trees and 3-trees.