Divisibility of certain coefficients of the chromatic polynomials

Abstract

The divisibility of certain coefficient of the chromatic polynomials was discussed. It is found that G was considered as a graph with vertex set V(G) and edge set, and of order n (=|V(G)|)and size m (=|E(G)|). The number of spanning subgraphs of G that had exactly n - i edges and that contained no broken cycles was counted. Results shows that when G was uniquely k-colorable graph, where k≥2, then a1(G) was divisible by (k - 1)!.