Chromatic polynomials of generalized trees

Abstract This paper is a survey of results on chromatic polynomials of graphs which are generalizations of trees. In particular, chromatic polynomials of q -trees will be discussed. The smallest q -tree ( q ≥1) is the complete graph K q on q vertices. A q -tree on n +1 vertices where n ≥ q , is obtained by adding a new vertex adjacent to each of q arbitrarily selected, mutually adjacent vertices in a q -tree on n vertices. Another generalization of trees is the n -gon-trees. The smallest n -gon-tree ( n ≥3) is the n -gon which is a cycle of n vertices. A n -gon-tree with k +1 n -gons is obtained from a n -gon-tree with k n -gons by adding a new n -gon which has exactly one edge in common with any n -gon of a n -gon-tree with k n -gons.