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A directed graph with three vertices and four directed edges (the double arrow represents an edge in each direction). A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising:
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 neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v. The neighbourhood is often denoted or (when the graph is unambiguous) . The same neighbourhood notation may also be used ...
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).
Let G be a simple plane graph with n vertices; we may add edges if necessary so that G is a maximally plane graph. If n < 3, the result is trivial. If n ≥ 3, then all faces of G must be triangles, as we could add an edge into any face with more sides while preserving planarity, contradicting the assumption of maximal planarity.
An independent set of ⌊ ⌋ vertices (where ⌊ ⌋ is the floor function) in an n-vertex triangle-free graph is easy to find: either there is a vertex with at least ⌊ ⌋ neighbors (in which case those neighbors are an independent set) or all vertices have strictly less than ⌊ ⌋ neighbors (in which case any maximal independent set must have at least ⌊ ⌋ vertices). [4]
This sortable list points to the articles describing various individual (finite) graphs. [1] 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.
The different types of edge in a bidirected graph. In the mathematical domain of graph theory, a bidirected graph (introduced by Edmonds & Johnson 1970) [1] is a graph in which each edge is given an independent orientation (or direction, or arrow) at each end. Thus, there are three kinds of bidirected edges: those where the arrows point outward ...