an:03918392
Zbl 0575.05027
Chao, Chongyun; Li, Nianzu
On trees of polygons
EN
Arch. Math. 45, 180-185 (1985).
00149639
1985
j
05C15
n-gon-trees; chromatic polynomial
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)].]
R.C.Read
Zbl 0218.05056