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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
M Salman A.N.
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia
Electrical & Electronics Engineering

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Upper bounds of the strong 3-rainbow index of corona product graphs M Salman A.N.; Zata Yumni Awanis; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (2026): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2026.14.2.1

Abstract

A tree in an edge-colored connected graph G of order n, where adjacent edges may be colored the same, is a rainbow tree if no two of its edges have the same color. Let k be an integer with 2 ≤ k ≤ n. An edge-coloring of G is called a strong k-rainbow coloring of G if for every S ⊆ V(G) with |S| = k, there exists a rainbow tree of minimum size connecting S. The minimum number of colors that are needed such that G admits a strong k-rainbow coloring is called the strong k-rainbow index of G, denoted by srxk(G). In this paper, we study the srx3 of corona product between two connected graphs G and H, denoted by G ⊙ H. We first provide an algorithm to define a strong 3-rainbow coloring of G ⊙ H. Hence, we obtain a sharp upper bound for srx3(G ⊙ H). We also characterize graphs H with srx3(Tn ⊙ H) equals the upper bound.
Co-Authors Suhadi Wido Saputro Zata Yumni Awanis