Neighborhood Total Domination and Colouring in Graphs
C. Sivagnanam · International Journal of Mathematics and Soft Computing · 2015
Let G= (V,E) be a graph without isolated vertices. A dominating set S of G is a neighbourhood total dominating set (ntd-set) if the induced subgraph of G has no isolated vertices. The neighbourhood total domination number is the minimum cardinality of a ntd-set. The minimum number of colours required to colour all the vertices such that no two adjacent vertices have the same colour is the chromatic number of G. In this paper we find an upper bound for sum of the ntd –number and chromatic number and characterize the corresponding extremal graphs.