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The mathematical study of the properties of the formal mathematical structures called graphs.

The multiplicity of a multigraph is its maximum edge multiplicity.

The Hamiltonian number h(n) of a connected graph G is the length of a Hamiltonian walk G. In other words, it is the minimum length of a closed spanning walk in the graph. For ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

For a connected bipartite graph G, the halved graph G^+ and G^- are the two connected components of the distance 2-graph of G. The following table summarizes some named ...

The Mathon graphs are three strongly regular graphs on 784 vertices with regular parameters as summarized in the following tables. k spectrum regular parameters 0 ...

The Tutte 8-cage (Godsil and Royle 2001, p. 59; right figure) is a cubic graph on 30 nodes and 45 edges which is the Levi graph of the Cremona-Richmond configuration. It ...

A set of graph vertices A of a graph with graph edges V is independent if it contains no graph edges.

Petersen's theorem states that every cubic graph with no bridges has a perfect matching (Petersen 1891; Frink 1926; König 1936; Skiena 1990, p. 244). In fact, this theorem ...

A graph G is the edge graph of a polyhedron iff G is a simple planar graph which is 3-connected.