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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 ...
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 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 .
For instance, in the octahedron graph, shown in the figure, each vertex has a neighbourhood isomorphic to a cycle of four vertices, so the octahedron is locally C 4. For example: Any complete graph K n is locally K n-1. The only graphs that are locally complete are disjoint unions of complete graphs. A Turán graph T(rs,r) is locally T((r-1)s,r ...
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
class 1. A class of graphs or family of graphs is a (usually infinite) collection of graphs, often defined as the graphs having some specific property. The word "class" is used rather than "set" because, unless special restrictions are made (such as restricting the vertices to be drawn from a particular set, and defining edges to be sets of two ...
If path ends at vertex , then the vertex corresponding to in has degree equal to the number of ways that may be extended by an edge that does not connect back to ; that is, the degree of this vertex in is either (an even number) if does not form part of a Hamiltonian cycle through , or (an odd number) if is part of a Hamiltonian cycle ...
In mathematics, calculus on finite weighted graphs is a discrete calculus for functions whose domain is the vertex set of a graph with a finite number of vertices and weights associated to the edges.
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