Geodesic
More on the Minimum Size of Graphs with Given Rainbow Index
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 227-241.

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The concept of k-rainbow index rxk(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, ℓ) to investigate the problems of the minimum size of a connected graph with given order and k-rainbow index at most ℓ and obtained some exact values and upper bounds for t(n, k, ℓ). In this paper, we obtain some exact values of t(n, k, ℓ) for large ℓ and better upper bounds of t(n, k, ℓ) for small ℓ and k = 3.
Keywords: Steiner distance, rainbow S -tree, k -rainbow index 
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Zhao, Yan. More on the Minimum Size of Graphs with Given Rainbow Index. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 227-241. http://geodesic.mathdoc.fr/item/DMGT_2020_40_1_a14/

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