| Autor: |
Septyanto, Fendy |
| Předmět: |
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| Zdroj: |
AIP Conference Proceedings; 2024, Vol. 3176 Issue 1, p1-6, 6p |
| Abstrakt: |
In an edge labeled graph, a rainbow path is a path whose edge colors are all distinct. An edge labeling such that every pair of distinct vertices can be connected by a rainbow path is called rainbow coloring. The smallest number of colors in a rainbow coloring of a graph 퐺 is called its rainbow connection number, denoted by 푟푐(퐺). A subgraph 퐻 of 퐺 is 2-dominating if every vertex of 퐺 outside of 퐻 has at least two neighbors in 퐻. In this paper, we prove the bound 푟푐(퐺) ≤ 푟푐(퐻) + 2 if 퐻 is a connected 2-dominating subgraph of 퐺. The method we use is extending a rainbow coloring of the subgraph to a rainbow coloring of the entire graph. We also use the bound to complete our previous investigation of the rainbow connection number of sequential join. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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