Search Results for ""

The degree of a graph vertex v of a graph G is the number of graph edges which touch v. The vertex degrees are illustrated above for a random graph. The vertex degree is also ...

The toroidal crossing number cr_(1)(G) of a graph G is the minimum number of crossings with which G can be drawn on a torus. A planar graph has toroidal crossing number 0, ...

The traveling salesman problem is a problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian cycle a salesman can take through each of n ...

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs G and H with graph vertices ...

König's line coloring theorem states that the edge chromatic number of any bipartite graph equals its maximum vertex degree. In other words, every bipartite graph is a class ...

The edge connectivity, also called the line connectivity, of a graph is the minimum number of edges lambda(G) whose deletion from a graph G disconnects G. In other words, it ...

Let G be a k-regular graph with girth 5 and graph diameter 2. (Such a graph is a Moore graph). Then, k=2, 3, 7, or 57. A proof of this theorem is difficult (Hoffman and ...

Isomorphic factorization colors the edges a given graph G with k colors so that the colored subgraphs are isomorphic. The graph G is then k-splittable, with k as the divisor, ...

A tree is a mathematical structure that can be viewed as either a graph or as a data structure. The two views are equivalent, since a tree data structure contains not only a ...

The circuit rank gamma, also denoted mu (Volkmann 1996, Babić et al. 2002) or beta (White 2001, p. 56) and known as the cycle rank (e.g., White 2001, p. 56), (first) graph ...