Open AccessGraphs with strong 3-rainbow index equals 2
Author(s) -
A. N. M. Salman,
Zata Yumni Awanis,
Suhadi Wido Saputro
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2157/1/012011
Subject(s) - combinatorics , rainbow , mathematics , colored , graph , upper and lower bounds , edge coloring , connectivity , discrete mathematics , graph power , physics , line graph , mathematical analysis , materials science , quantum mechanics , composite material
Let G be an edge-colored connected graph of order n ≥ 3, where adjacent edges may be colored the same. Let k be an integer with 2 ≤ k ≤ n and S ⊆ V ( G ) with | S | = k . The Steiner distance d ( S ) of S is the minimum size of a tree in G connecting S . The strong k -rainbow index srx k ( G ) of G is the minimum number of colors required to color the edges of G so that every set S in G is connected by a tree of size d ( S ) whose edges have distinct colors. We focus on k = 3. In this paper, we first characterize the graphs G with srx 3 ( G ) = 2. According to the definition, it is clearly that ‖ G ‖ is the trivial upper bound for srx 3 ( G ). Several previous researchers have shown that there exist some connected graphs G such that srx 3 ( G ) = ‖ G ‖. Hence, in this paper, we provide another graph G such that srx 3 ( G ) = ‖ G ‖.