Generalised colouring sums of graphs

Johan Kok (1) , Sudev Naduvath (1) , K. P. Chithra (1)

1 Christ University, Bangalore

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.

Mots clés: Chromatic number; χ + -chromatic sum; χ-chromatic sum; b-chromatic number; b-chromatic sum; b + -chromatic sum; Thue chromatic number; π + - chromatic sum; π-chromatic sum

Domaines: Combinatoire [math.CO]

Johan Kok, Sudev Naduvath, K. P. Chithra. Generalised colouring sums of graphs. Cogent Mathematics & Statistics, 2016, 3 (1), pp.1140002. ⟨10.1080/23311835.2016.1140002⟩. ⟨hal-02263314⟩