MAKASSAR, Indonesia May 2 2026/graphtheory/ Traffic congestion is not only a daily inconvenience. It can waste fuel, increase travel time, raise stress levels, and reduce the efficiency of public services. Researchers often use mathematics to understand such problems before new systems are built. One useful approach comes from graph theory, a branch of mathematics that represents places as points and routes as connecting lines.
The article “Development of Navigation Systems in Optimal Utilization of Transportation Routes in Topology Helm Graphs Using Graph Labeling” studies a special network model called a modified helm graph. Although the name sounds technical, the basic idea is simple. Imagine a circular road network with several connected branches. Each intersection is represented by a vertex, while each road is represented by an edge. By assigning numbers to both vertices and edges, researchers can create unique numerical identities for every point in the network.
This process is known as total vertex irregular labeling. The number assigned to a vertex is added to the numbers on all roads connected to it. The final sum is called the vertex weight. A successful labeling gives every vertex a different weight. In practical terms, this is similar to ensuring that every intersection in a navigation system has its own unmistakable code, even when the road pattern is highly repetitive.
The researchers focused on finding the smallest range of numbers needed to produce these unique identities. This minimum value is called the total vertex irregularity strength. For the modified helm graph studied in the article, they proved that the value can be calculated using the formula:
Here, represents the size of the repeating part of the network, while the ceiling symbol means that the result is rounded up to the nearest whole number. The researchers established both a lower limit and an upper limit, then showed that the two limits were equal. This confirmed the exact formula for every valid network size.
The value of this finding is mainly theoretical, but it provides a foundation for future navigation and transportation algorithms. A clear labeling pattern could help computer systems distinguish intersections, organize route data, reduce ambiguity, and process complex network structures more efficiently. However, the article does not report a field-tested navigation application; instead, it develops the mathematical framework needed for later practical research.
This study can be linked directly to Sustainable Development Goal 3: Good Health and Well-Being. Better transportation planning may help reduce long periods spent in traffic, lower driver stress, support faster emergency response, and contribute to safer urban mobility. Mathematics alone cannot solve congestion, but it can provide reliable models for designing smarter systems.
Ultimately, the research shows that numbers placed carefully on a network can do more than solve an abstract puzzle. They can become the language through which future navigation systems understand complicated roads and make transportation routes easier to manage.
Reference:
DOI: https://doi.org/10.55214/25768484.v9i1.4161
Contact:
Prof. Nurdin
+62 813-9519-0801
nurdin1701@unhas.ac.id
