Colouring of Linguistic Z-graph and Its Application

In this study, we introduce an innovative approach for representing uncertainty in graph structures through linguistic Z-graphs (LZGs). Linguistic Z-number theory offers a comprehensive framework for capturing and quantifying uncertainty in graph-based models. The core idea behind LZG is to integrate linguistic variables into the representation of uncertainty, thereby providing a more expressive and intuitive means of analysis. Graph colouring is a big deal in graph theory because it solves many real problems like traffic lights, maps, and schedules. This study introduced a new concept of LZG for graph colouring. Chromatic numbers and strong chromatic numbers are defined differently and learn more about them. An application is presented using the colouring of LZGs.