Clique-width is a graph parameter that provides a measure of the complexity of a graph in terms of its structure related to cliques (complete subgraphs). It plays a significant role in graph theory, particularly in the context of algorithm design and graph algorithms. A graph has clique-width \(k\) if it can be constructed using a specific process that involves the following operations: 1. **Creation of a new vertex (a single vertex graph)**.
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