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A quartic symmetric graph is a symmetric graph that is also quartic (i.e., regular of degree 4). The numbers of symmetric quartic graphs on n=1, 2, ... are 0, 0, 0, 0, 1, 1, ...

A complete metric is a metric in which every Cauchy sequence is convergent. A topological space with a complete metric is called a complete metric space.

The bandwidth of a connected graph G is the minimum matrix bandwidth among all possible adjacency matrices of graphs isomorphic to G. Equivalently, it is the minimum graph ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

The Kuratowski reduction theorem states that very nonplanar graph contains either the utility graph UG=K_(3,3) or the pentatope graph K_5 as a graph minor. The graphs K_(3,3) ...

"The" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party ...

Every planar graph (i.e., graph with graph genus 0) has an embedding on a torus. In contrast, toroidal graphs are embeddable on the torus, but not in the plane, i.e., they ...

If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a ...

The Harary graph H_(k,n) is a particular example of a k-connected graph with n graph vertices having the smallest possible number of edges. The smallest number of edges ...