Strong 3-Rainbow Indexes of Closed Helm Graphs

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