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A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
The graph can be constructed from a single vertex by a sequence of operations that add a new degree-one (pendant) vertex, or duplicate (twin) an existing vertex, with the exception that a twin operation in which the new duplicate vertex is not adjacent to its twin (false twins) can only be applied when the neighbors of the twins form a clique.
A vertex with degree 1 is called a leaf vertex or end vertex or a pendant vertex, and the edge incident with that vertex is called a pendant edge. In the graph on the right, {3,5} is a pendant edge. This terminology is common in the study of trees in graph theory and especially trees as data structures .
1. A leaf vertex or pendant vertex (especially in a tree) is a vertex whose degree is 1. A leaf edge or pendant edge is the edge connecting a leaf vertex to its single neighbour. 2. A leaf power of a tree is a graph whose vertices are the leaves of the tree and whose edges connect leaves whose distance in the tree is at most a given threshold.
The midheaven (also known as the "medium coeli") is the point where the ecliptic crosses the local meridian; it is used in the construction of a horoscope/natal chart Vertex: Vx or : Vx or 🜊 U+1F70A: The vertex and anti-vertex are the points where the prime vertical intersects the ecliptic.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A gear graph, denoted G n, is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a wheel graph W n. Thus, G n has 2n+1 vertices and 3n edges. [4] Gear graphs are examples of squaregraphs, and play a key role in the forbidden graph characterization of squaregraphs. [5]
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