Abstract
We introduce a strong \(k\)-rainbow index of graphs as modification of well-known \(k\)-rainbow index of graphs. A tree in an edge-colored connected graph \(G\), where adjacent edge may be colored the same, is a rainbow tree if all of its edges have distinct colors. Let \(k\) be an integer with \(2\leq k\leq n\). The strong \(k\)-rainbow index of \(G\), denoted by \(srx_k(G)\), is the minimum number of colors needed in an edge-coloring of \(G\) so that every \(k\) vertices of \(G\) is connected by a rainbow tree with minimum size. We focus on \(k=3\). We determine the strong \(3\)-rainbow index of some certain graphs. We also provide a sharp upper bound for the strong \(3\)-rainbow index of amalgamation of graphs. Additionally, we determine the exact values of the strong \(3\)-rainbow index of amalgamation of some graphs.
Publisher
AGHU University of Science and Technology Press
Cited by
3 articles.
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1. On the locating rainbow connection number of amalgamation of complete graphs;Journal of Physics: Conference Series;2023-07-01
2. Rainbow connection number of comb product of graphs;Electronic Journal of Graph Theory and Applications;2022-09-25
3. Graphs with strong 3-rainbow index equals 2;Journal of Physics: Conference Series;2022-01-01