Graph homomorphism

Graph homomorphism is a way of matching up the points (or "nodes") of one graph to the points of another graph in a special way.

Imagine two graphs like puzzles. One puzzle has ten pieces, and the other puzzle has eight pieces. In a graph homomorphism, we figure out how to map the ten pieces from the first puzzle to the eight pieces of the second puzzle.

Each piece in each puzzle is a "node", and the connections between pieces are called "edges". When we map one piece from the first puzzle to a piece in the second puzzle, we try to make sure that the connections (edges) line up too. For example, if two pieces in the first puzzle are connected by an edge, we try to find two pieces in the second puzzle that are also connected by an edge.

This way, every connection in the first puzzle matches with a connection in the second puzzle. This is what "homomorphism" means. When two graphs are related in this way, it is called a graph homomorphism.