Chromatic polynomials with least coefficients Original Research Article

In this paper, we characterize the n-point e-edge graphs G that minimize the absolute values ai(G) of the coefficients of the chromatic polynomial P(G; λ) = ∑ni=1(−1)n−iai(G)λi. Let Ω(n, e) be the collection of all connected n-point, e-edge graphs. For a given i, we say that a graph G ∈ Ω(n,e) is ai-minimum if ai(G)⩽ai(G′) for all G′ ∈ Ω(n,e). We show that a graph is ai-minimum iff it is ai−1-minimum for all 2⩽i⩽n−2.