Strong 3-Rainbow Indexes of Closed Helm Graphs

Nugrahani, Calista Suci (Institut Teknologi Bandung)
Constantine, Christian (Institut Teknologi Bandung)
Salman, A. N. M. (Institut Teknologi Bandung)

Indonesian Journal of Combinatorics
Vol 8, No 2 (2024)

Let G be a nontrivial, edge-colored, and connected graph of order m≥3 where adjacent edges may have the same color. A tree T in graph G is called a rainbow tree if all the edges in T have different colors. For S⊆V(G), the Steiner distance sd(S) of S is the minimum size of a tree in G containing S. Let k be an integer with 2≤k≤m. An edge-coloring in G is a strong k-rainbow coloring if for every set S of k vertices of G, there exists a rainbow tree of size sd(S) in G containing S. In this paper, we study the strong 3-rainbow index (srx3) of Closed Helm graph. We also determine the srx3 of Closed Helm graph.