We determine the smallest and the largest number of -edge colourings in trees. We prove that the star is a unique tree that maximizes the number of all of the -edge colourings and that the path is a unique tree that minimizes it.
Krzysztof Piejko. "Extremal Trees with respect to Number of -Edge Colourings." J. Appl. Math. 2015 1 - 5, 2015. https://doi.org/10.1155/2015/463650