Novel representation of complexity of investment casting using injective coloring and graph adaptive consensus mechanism

The complexity of industrial investment casting is determined by three factors related to geometry, desired features, and manufacturability that are further driven by 19 elements, 52 attributes, and 212 meta-attributes. The complexity of the investment casting process is calculated using one of the important multi-criteria decision-making methods, such as the analytical hierarchy process. The complexity helps to make decisions about producing industrial casting using investment casting, the impact of any individual parameter, as well as the dependency of individual parameters on the overall process. However, representing complexity for easy understanding is challenging. The researchers explored various approaches, but graph theory in injective coloring remains unexplored in published literature. This paper presents a solution to the problem of representing the complexity index in graph-based systems that leverage both a graph theory adaptive consensus mechanism algorithm and injective coloring. The proposed approach guarantees effective node representations and is robust enough to identify the maximum and minimum complexity values of a particular parameter on the graph. By applying injective coloring, collection conflict is minimized and node differentiation is extended, allowing critical components of the network to be easily located. The adaptive consensus mechanism algorithm readily adapts to a varying graph structure to create scalability and efficiency.