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A nonplanar graph G is said to be critical nonplanar if the removal of a vertex results in a planar graph for every vertex of G. Critical nonplanar graphs differ from apex ...

A cyclic graph is a graph containing at least one graph cycle. A graph that is not cyclic is said to be acyclic. A cyclic graph possessing exactly one (undirected, simple) ...

The group C_2 is the unique group of group order 2. C_2 is both Abelian and cyclic. Examples include the point groups C_s, C_i, and C_2, the integers modulo 2 under addition ...

A graph G is said to be disconnected if it is not connected, i.e., if there exist two nodes in G such that no path in G has those nodes as endpoints. The numbers of ...

Every finite simple group (that is not cyclic) has even group order, and the group order of every finite simple noncommutative group is doubly even, i.e., divisible by 4 ...

A graph with a finite number of nodes and edges. If it has n nodes and has no multiple edges or graph loops (i.e., it is simple), it is a subgraph of the complete graph K_n. ...

Gaussian brackets are notation published by Gauss in Disquisitiones Arithmeticae and defined by [ ]=1 (1) [a_1]=a_1 (2) [a_1,a_2]=[a_1]a_2+[ ] (3) ...

Let V(G) be the vertex set of a simple graph and E(G) its edge set. Then a graph isomorphism from a simple graph G to a simple graph H is a bijection f:V(G)->V(H) such that ...

A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions. For an abstract algebraic curve, if x and y are nonconstant ...

Call a graph vertex m(a,b,c) a median of a graph G if it lies on all shortest paths between each pair of vertices (a,b), (b,a), and (c,a) in G. A median graph is then defined ...