Strong 3-Rainbow Indexes of Closed Helm Graphs

Abstract

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.