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A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

A simple path is a path which is a simple curve. More precisely, a continuous mapping gamma:[a,b]->C^0 is a simple path if it has no self-intersections. Here, C^0 denotes the ...

The path of an object through phase space.

A shortest path between two vertices of a graph is a graph path of shortest possible length between them. Such paths are also known as graph geodesics, and the matrix giving ...

The all-pairs shortest path problem is the determination of the shortest graph distances between every pair of vertices in a given graph. The problem can be solved using n ...

A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose ...

The longest path problem asks to find a path of maximum length in a given graph. The problem is NP-complete, but there exists an efficient dynamic programming solution for ...

The image of the path gamma in C under the function f is called the trace. This usage of the term "trace" is unrelated to the same term applied to matrices or tensors.

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a path polynomial whose coefficients are the numbers of paths of ...

The path graph P_n is a tree with two nodes of vertex degree 1, and the other n-2 nodes of vertex degree 2. A path graph is therefore a graph that can be drawn so that all of ...