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A labeled tree is a tree in which each vertex is given a unique label. The vertices of a labeled tree on n vertices (for nonnegative integers n) are typically given the labels 1, 2, …, n. A recursive tree is a labeled rooted tree where the vertex labels respect the tree order (i.e., if u < v for two vertices u and v, then the label of u is ...
A graph with 16 vertices and six bridges (highlighted in red) An undirected connected graph with no bridge edges. In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. [1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle.
A grader, also commonly referred to as a road grader, motor grader, or simply blade, is a form of heavy equipment with a long blade used to create a flat surface during grading. Although the earliest models were towed behind horses, and later tractors , most modern graders are self-propelled and thus technically "motor graders".
[9] [10] If the edges of the graph are given positive weights, the minimum weight basis of the cut space can be described by a tree on the same vertex set as the graph, called the Gomory–Hu tree. [11] Each edge of this tree is associated with a bond in the original graph, and the minimum cut between two nodes s and t is the minimum weight ...
2. A rooted tree structure used to describe a cograph, in which each cograph vertex is a leaf of the tree, each internal node of the tree is labeled with 0 or 1, and two cograph vertices are adjacent if and only if their lowest common ancestor in the tree is labeled 1. cover A vertex cover is a set of vertices incident to every edge in a graph.
Section through railway track and foundation showing the sub-grade. Grading in civil engineering and landscape architectural construction is the work of ensuring a level base, or one with a specified slope, [1] for a construction work such as a foundation, the base course for a road or a railway, or landscape and garden improvements, or surface drainage.
Euler's formula can also be proved as follows: if the graph isn't a tree, then remove an edge which completes a cycle. This lowers both e and f by one, leaving v – e + f constant. Repeat until the remaining graph is a tree; trees have v = e + 1 and f = 1, yielding v – e + f = 2, i. e., the Euler characteristic is 2.
Trees with a single root may be viewed as rooted trees in the sense of graph theory in one of two ways: either as a tree (graph theory) or as a trivially perfect graph. In the first case, the graph is the undirected Hasse diagram of the partially ordered set, and in the second case, the graph is simply the underlying (undirected) graph of the ...