Generalised colouring sums of graphs.

The notion of the b-chromatic number of a graph attracted much research interests and recently a new concept, namely the b-chromatic sum of a graph, denoted by φ'(G), has also been introduced. Motivated by the studies on b-chromatic sum of graphs, in this paper we introduce certain new parameters such as χ-chromatic sum, χ+-chromatic sum, b+-chromatic sum, π-chromatic sum and π+-chromatic sum of graphs. We also discuss certain results on these parameters for a selection of standard graphs. [ABSTRACT FROM AUTHOR]