Modeling traffic-light systems: A neutrosophic graph approach

Abstract

The coloring of neutrosophic graphs (NGs) is an important concept with extensive real-world applications. This research focuses on chromatic numbers for NGs and their operations. We define the neutrosophic chromatic number based on the alpha-, beta-, and gamma-cuts, as well as the strong alpha-, beta-, and gamma-cuts, of an NG. Furthermore, a comparative analysis of the proposed neutrosophic chromatic number is performed using the neutrosophic independent vertex set, demonstrating the effectiveness of the proposed approach. Several properties related to the union of NGs are also investigated using the proposed neutrosophic chromatic number. Finally, an illustrative traffic-light case study demonstrates the applicability of the proposed graph-coloring framework. The case study shows how the framework can model uncertain traffic conflicts and determine the minimum number of signal phases required for safe traffic operation. In the illustrative example, the obtained neutrosophic chromatic numbers indicate that the traffic network can be managed using five (k=5) signal phases under the proposed model, illustrating the framework's potential for efficient traffic-light scheduling, the reduction of potential traffic conflicts, and support for intelligent traffic-management decisions under uncertainty.