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Updated: Jun 24, 2025
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Optimization of Synthetic Proteins: Identification of Interpositional Dependencies Indicating Structurally and/or Functionally Linked Residues
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Rainbow connections of bioriented graphs
Linlin Wang1, Sujuan Liu2, Han Jiang2
1School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
Heliyon
|June 4, 2024
Summary
This study explores graph coloring, specifically the rainbow connection number and total rainbow connection number for directed graphs. It investigates these concepts for the biorientation of connected graphs, determining the minimum colors needed for unique path and vertex coloring.
Area of Science:
- Graph Theory
- Discrete Mathematics
- Network Science
Background:
- Rainbow connectivity requires distinct arc colors for all paths between any two vertices.
- The rainbow connection number is the minimum colors for rainbow connectivity.
- Total coloring involves unique colors for both arcs and internal vertices.
Purpose of the Study:
- Investigate the rainbow connection number of graph biorientations.
- Determine the total rainbow connection number for these structures.
Main Methods:
- Analyzing properties of directed graphs and their biorientations.
- Applying concepts of graph coloring and path enumeration.
- Calculating minimum color requirements for specific graph structures.
Main Results:
- The study provides insights into the rainbow connection number for biorientations.
- It establishes findings related to the total rainbow connection number in these graphs.
Conclusions:
- The research contributes to understanding the complexity of rainbow coloring in directed graphs.
- It offers foundational results for further exploration of total rainbow connection numbers.
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