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A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. [1] [2] [3]
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 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 degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices. In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is n(n − 1) / 2 .
A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible.. In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
A vertex with deg − (v) = 0 is called a source, as it is the origin of each of its outcoming arcs. Similarly, a vertex with deg + (v) = 0 is called a sink, since it is the end of each of its incoming arcs. The degree sum formula states that, for a directed graph,
A graceful labeling; vertex labels are in black and edge labels in red. A graph is known as graceful if its vertices are labeled from 0 to | E |, the size of the graph, and if this vertex labeling induces an edge labeling from 1 to | E |. For any edge e, the label of e is the positive difference between the labels of the two vertices incident ...
V7 is an isolated vertex. Vertices are aligned to the left. The legend on the right shows the names of the edges. An example of a directed hypergraph, ...