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Example of an undirected multigraph with 3 vertices, 3 edges and 4 loops. For vertices A,B,C and D, the degrees are respectively 4,4,5,1 For vertices U,V,W and X, the degrees are 2,2,3 and 1 respectively.
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 ...
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).
The columns 'vertices', 'edges', 'radius', 'diameter', 'girth', 'P' (whether the graph is planar), χ (chromatic number) and χ' (chromatic index) are also sortable, allowing to search for a parameter or another.
As special cases, the order-zero graph (a forest consisting of zero trees), a single tree, and an edgeless graph, are examples of forests. Since for every tree V − E = 1, we can easily count the number of trees that are within a forest by subtracting the difference between total vertices and total edges. V − E = number of trees in a forest.
This hypergraph has order 7 and size 4. Here, edges do not just connect two vertices but several, and are represented by colors. Alternative representation of the hypergraph reported in the figure above, called PAOH. [1] Edges are vertical lines connecting vertices. V7 is an isolated vertex. Vertices are aligned to the left.
where V is the number of vertices, E is the number of edges, and F is the number of faces. This equation is known as Euler's polyhedron formula. Thus the number of vertices is 2 more than the excess of the number of edges over the number of faces. For example, since a cube has 12 edges and 6 faces, the formula implies that it has eight vertices.
[5] A line graph has an articulation point if and only if the underlying graph has a bridge for which neither endpoint has degree one. [2] For a graph G with n vertices and m edges, the number of vertices of the line graph L(G) is m, and the number of edges of L(G) is half the sum of the squares of the degrees of the vertices in G, minus m. [6]
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