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Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

A subset G subset R of the real numbers is said to be a G_delta set provided G is the countable intersection of open sets. The name G_delta comes from German: The G stands ...

Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...

The eigenvalues of a graph are defined as the eigenvalues of its adjacency matrix. The set of eigenvalues of a graph is called a graph spectrum. The largest eigenvalue ...

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 ...

There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. In fact, the problem of identifying ...

An orientation of an undirected graph G is an assignment of exactly one direction to each of the edges of G. Only connected, bridgeless graphs can have a strong orientation ...

The radius of a graph is the minimum graph eccentricity of any graph vertex in a graph. A disconnected graph therefore has infinite radius (West 2000, p. 71). Graph radius is ...

The union G=G_1 union G_2 of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph with V=V_1 union V_2 and X=X_1 union X_2 (Harary ...

Suppose that G is a pseudograph, E is the edge set of G, and C is the family of edge sets of graph cycles of G. Then C obeys the axioms for the circuits of a matroid, and ...