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A strongly connected digraph is a directed graph in which it is possible to reach any node starting from any other node by traversing edges in the direction(s) in which they ...

"Vertex" is a synonym for a node of a graph, i.e., one of the points on which the graph is defined and which may be connected by graph edges. The terms "point," "junction," ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

A search algorithm of a tree that explores the first child of a node before visiting its siblings. Tarjan (1972) and Hopcroft and Tarjan (1973) showed that depth-first search ...

The Laplacian matrix, sometimes also called the admittance matrix (Cvetković et al. 1998, Babić et al. 2002) or Kirchhoff matrix, of a graph G, where G=(V,E) is an ...

A leaf of an unrooted tree is a node of vertex degree 1. Note that for a rooted or planted tree, the root vertex is generally not considered a leaf node, whereas all other ...

A rooted tree is a tree in which a special ("labeled") node is singled out. This node is called the "root" or (less commonly) "eve" of the tree. Rooted trees are equivalent ...

A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon. If each point of intersection is associated with a node and diagonals are split ar each ...

A tree (also called a central tree) having a single node that is a graph center. The numbers of centered trees on n=1, 2, ... nodes are 1, 0, 1, 1, 2, 3, 7, 12, 27, 55, 127, ...