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All Journal Indonesian Journal of Combinatorics
Constantine, Christian
Institut Teknologi Bandung
Computer Science & IT Decision Sciences, Operations Research & Management

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Strong 3-Rainbow Indexes of Closed Helm Graphs Nugrahani, Calista Suci; Constantine, Christian; Salman, A. N. M.
Indonesian Journal of Combinatorics Vol 8, No 2 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.2.5

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.
Co-Authors Nugrahani, Calista Suci Salman, A. N. M.