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The unique 8_3 configuration. It is transitive and self-dual, but cannot be realized in the real projective plane. Its Levi graph is the Möbius-Kantor graph.

The Randić energy of a graph is defined as the graph energy of its Randić matrix, i.e., the sum of the absolute values of the eigenvalues of its Randić matrix.

The Sombor index of a graph is defined as half the sum of the matrix elements of its Sombor matrix.

A quasi-regular graph is a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 (Bozóki et al. 2020). ...

An ungraceful graph is a simple graph that does not possess a graceful labeling, i.e., a graph that is not a graceful graph (Gardner 1972). Such graphs have also been termed ...

There are two distinct notions of connectivity in a directed graph. A directed graph is weakly connected if there is an undirected path between any pair of vertices, and ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...

A giraffe graph is a graph formed by all possible moves of a hypothetical chess piece called a "giraffe" which moves analogously to a knight except that it is restricted to ...

A Hamiltonian walk on a connected graph is a closed walk of minimal length which visits every vertex of a graph (and may visit vertices and edges multiple times). For ...

If an infinite number of points in the plane are all separated by integer distances, then all the points lie on a straight line.