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An isolated point of a graph is a node of degree 0 (Hartsfield and Ringel 1990, p. 8; Harary 1994, p. 15; D'Angelo and West 2000, p. 212; West 2000, p. 22). The number of ...

A local sink is a node of a directed graph with no exiting edges, also called a terminal (Borowski and Borwein 1991, p. 401; left figure). A global sink (often simply called ...

A weakly connected digraph is a directed graph in which it is possible to reach any node starting from any other node by traversing edges in some direction (i.e., not ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

It is conjectured that every tree with e edges whose nodes are all trivalent or monovalent can be given a "magic" labeling such that the integers 1, 2, ..., e can be assigned ...

A tree which is not rooted, i.e., a normal tree with no node singled out for special treatment (Skiena 1990, p. 107). Free trees are sometimes known instead as unrooted trees ...

A search algorithm of a graph which explores all nodes adjacent to the current node before moving on. For cyclic graphs, care must be taken to make sure that no nodes are ...

Two nodes connected to the same node which are same distance from the root vertex in a rooted tree are called siblings. A function to return the siblings of a vertex v in a ...

A simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence, so that two edges (v_1,v_2) and (v_2,v_3) joined by a node v_2 of ...

A polyhedral graph is completely regular if the dual graph is also regular. There are only five types. Let rho be the number of graph edges at each node, rho^* the number of ...