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The blossom algorithm (Edmonds 1965) finds a maximum independent edge set in a (possibly weighted) graph. While a maximum independent edge set can be found fairly easily for ...

The Fano plane is the configuration consisting of the two-dimensional finite projective plane over GF(2) ("of order two"), illustrated above. It is a block design with nu=7, ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

The likelihood of a simple graph is defined by starting with the set S_1={(K_11)}. The following procedure is then iterated to produce a set of graphs G_n of order n. At step ...

Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

A point v is a central point of a graph if the eccentricity of the point equals the graph radius. The set of all central points is called the graph center.

Let a graph G have graph vertices with vertex degrees d_1<=...<=d_m. If for every i<n/2 we have either d_i>=i+1 or d_(n-i)>=n-i, then the graph is Hamiltonian.

A complete multipartite graph is a graph that is a complete k-partite graph for some positive integer k (Chartrand and Zhang 2008, p. 41).

A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.

An graph edge of a graph is separating if a path from a point A to a point B must pass over it. Separating graph edges can therefore be viewed as either bridges or dead ends.