Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth. Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. It is known that an (r,g)-graph exists for any combination of r >= 2 and g >= 3. An (r,g)-cage is an (r,g)-graph with the fewest possible number of vertices, among all (r,g)-graphs.

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