More on the minimum size of graphs with given rainbow index
Yan Zhao · Discussiones Mathematicae Graph Theory · 2018
The concept of k-rainbow index rx k (G) of a connected graph G, introduced by Chartrand et al., is a natural generalization of the rainbow connection number of a graph. Liu introduced a parameter t(n, k, ) to investigate the problems of the minimum size of a connected graph with given order and k-rainbow index at most and obtained some exact values and upper bounds for t(n, k, ). In this paper, we obtain some exact values of t(n, k, ) for large and better upper bounds of t(n, k, ) for small and k = 3.