A generalization of the chromatic polynomial of a cycle
Julian A. Allagan · DOAJ (DOAJ: Directory of Open Access Journals) · 2005
We prove that if an edge of a cycle on vertices is extended by adding vertices, then the the chromatic polynomial of such generalized cycle is: $$P(H_k,\lambda)=(\lambda-1)^n\sum_{i=0}^k \lambda^i+(-1)^n(\lambda-1).$$