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An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every finite acyclic digraph has at least one node of ...

The associated Stirling numbers of the first kind d_2(n,k)=d(n,k) are defined as the number of permutations of a given number n having exactly k permutation cycles, all of ...

The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...

Dijkstra's algorithm is an algorithm for finding a graph geodesic, i.e., the shortest path between two graph vertices in a graph. It functions by constructing a shortest-path ...

The term "Euler graph" is sometimes used to denote a graph for which all vertices are of even degree (e.g., Seshu and Reed 1961). Note that this definition is different from ...

A forest is an acyclic graph (i.e., a graph without any graph cycles). Forests therefore consist only of (possibly disconnected) trees, hence the name "forest." Examples of ...

Ore (1962) noted that not only does a tree possesses a unique shortest path between any two vertices, but that there also exist also other connected graphs having the same ...

Chvátal defines the term hole to mean "a chordless cycle of length at least four." The restriction "of length at least four" allows use of the term "hole" regardless of if ...

The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance ...

Order the natural numbers as follows: Now let F be a continuous function from the reals to the reals and suppose p≺q in the above ordering. Then if F has a point of least ...