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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 ...

Jung's theorem states that the generalized diameter D of a compact set X in R^n satisfies D>=Rsqrt((2(n+1))/n), where R is the circumradius of X (Danzer et al. 1963). This ...

In any tree, the number of dissimilar points minus the number of dissimilar lines plus the number of symmetry lines equals 1.

The treewidth is a measure of the count of original graph vertices mapped onto any tree vertex in an optimal tree decomposition. Determining the treewidth of an arbitrary ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

Searching refers to locating a given element or an element satisfying certain conditions from some (usually ordered or partially ordered) table, list, tree, etc.

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

A formal structure for the organization of information. Examples of data structures include the list, queue, stack, and tree.

The E graph is the tree on 6 vertices illustrated above. It is isomorphic to the (3,2)-firecracker graph and 3-centipede graph. It is implemented in the Wolfram Language as ...

For a given positive integer n, does there exist a weighted tree with n graph vertices whose paths have weights 1, 2, ..., (n; 2), where (n; 2) is a binomial coefficient? ...