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. |
Databáze: |
Directory of Open Access Journals |
Externí odkaz: |
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