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A semicomplete digraph is a quasi-transitive digraph. There are extensions of quasi-transitive digraphs called k-quasi-transitive digraphs. [5] Oriented graphs are directed graphs having no opposite pairs of directed edges (i.e. at most one of (x, y) and (y, x) may be arrows of the graph).
In mathematics, the free category or path category generated by a directed graph or quiver is the category that results from freely concatenating arrows together, whenever the target of one arrow is the source of the next. More precisely, the objects of the category are the vertices of the quiver, and the morphisms are paths between objects.
An acyclic directed graph, which is a digraph without directed cycles, is often called a directed acyclic graph, especially in computer science. [2] 2. An acyclic coloring of an undirected graph is a proper coloring in which every two color classes induce a forest. [3] adjacency matrix
The directed graph (or digraph) on the right is an orientation of the undirected graph on the left. In graph theory, an orientation of an undirected graph is an assignment of a direction to each edge, turning the initial graph into 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 best known vertex transitive digraphs (as of October 2008) in the directed Degree diameter problem are tabulated below. Table of the orders of the largest known vertex-symmetric graphs for the directed degree diameter problem
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]
A flow graph is more general than a directed network, in that the edges may be associated with gains, branch gains or transmittances, or even functions of the Laplace operator s, in which case they are called transfer functions. [2] There is a close relationship between graphs and matrices and between digraphs and matrices. [9] "The algebraic ...