# 5783

This number is a prime.

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In graph theory, 5783 is the number of distinct simple, connected, 20-vertex, degree-3 graphs with a girth of at least 5. To understand this more fully, recall these graph theory definitions:

- A "simple" graph has no multiple edges or loops. - A "connected" graph has a path (succession of edges) between any two vertices. - The "degree" of a vertex is the number of edges connected to it, and the degree of a graph is its highest vertex degree. - A "cycle" is a path that starts and ends at the same vertex V and never visits the same vertex twice (except for V). - The "girth" of a graph is the length (number of edges) of its shortest cycle.[Keith]

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