The strong 3-rainbow index of edge-comb product of a path and a connected graph

Autor: Zata Yumni Awanis, A.N.M. Salman, Suhadi Wido Saputro
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Electronic Journal of Graph Theory and Applications, Vol 10, Iss 1, Pp 33-50 (2022)
Druh dokumentu: article
ISSN: 2338-2287
DOI: 10.5614/ejgta.2022.10.1.3
Popis: Let G be a connected and edge-colored graph of order n, where adjacent edges may be colored the same. A tree in G is a rainbow tree if all of its edges have distinct colors. Let k be an integer with 2 ≤ k ≤ n. The minimum number of colors needed in an edge coloring of G such that there exists a rainbow tree connecting S with minimum size for every k-subset S of V(G) is called the strong k-rainbow index of G, denoted by srxk(G). In this paper, we study the srx3 of edge-comb product of a path and a connected graph, denoted by Pno⊳eH. It is clearly that |E(Pno⊳eH)| is the trivial upper bound for srx3(Pno⊳eH). Therefore, in this paper, we first characterize connected graphs H with srx3(Pno⊳eH)=|E(Pno⊳eH)|, then provide a sharp upper bound for srx3(Pno⊳eH) where srx3(Pno⊳eH)≠|E(Pno⊳eH)|. We also provide the exact value of srx3(Pno⊳eH) for some connected graphs H.
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