A graph homomorphism is a mapping between two graphs that preserves the structure of the graphs. Specifically, if there is an edge between two vertices in the first graph, the corresponding vertices in the second graph must also have an edge between them. This concept helps in understanding how different graphs can relate to each other while maintaining their connectivity properties. Graph homomorphisms are important in various fields, including computer science, mathematics, and network theory. They can be used to simplify complex problems by transforming them into more manageable forms, allowing researchers to analyze relationships and properties across different types of graphs.