On trees of polygons
The set S of n-gon-trees is defined recursively as follows: (a) The n-gon is in S. (b) If G is in S, then so is any graph formed by identifying an edge of G with an edge of an n-gon. The authors prove that a graph is an n-gon-tree on k n-gons if and only if its chromatic polynomial is \[ [(\lambda -1)^ n+(-1)^ n(\lambda -1)]^ k/[\lambda (\lambda - 1)]^{k-1}. \] [Reviewer's comments: The elaborate definition of \(Q(C_ n,\lambda)\) in Lemma 5 is unnecessary. Corollary 1.1 is a result due to \textit{G. H. J. Meredith} [J. Comb. Theory, Ser. B 13, 14-17 (1972; Zbl 0218.05056)].]
scientific article; zbMATH DE number 3918392