Chromatic bases for symmetric functions

In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if {G(k)}(k >= 1) is a set of connected graphs such that G(k) has k vertices for each k, then the set of all chromatic symmetric functions {XG(k)}(k >= 1) generates the algebra of symmetric functions. We also obtain explicit expressions for the generators arising from complete graphs, star graphs, path graphs and cycle graphs.