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A walk in a mixed graph is a sequence ,,,,, …,, of vertices and edges/arcs such that for every index , either = + is an edge of the graph or = + is an arc of the graph. This walk is a path if it does not repeat any edges, arcs, or vertices, except possibly the first and last vertices.
A graph is H-minor-free if it does not have H as a minor. A family of graphs is minor-closed if it is closed under minors; the Robertson–Seymour theorem characterizes minor-closed families as having a finite set of forbidden minors. mixed A mixed graph is a graph that may include both directed and undirected edges. modular 1.
X-bar theory graph of the sentence "He studies linguistics at the university." Constituency is a one-to-one-or-more relation; every word in the sentence corresponds to one or more nodes in the tree diagram. Dependency, in contrast, is a one-to-one relation; every word in the sentence corresponds to exactly one node in the tree diagram.
In statistics and Markov modeling, an ancestral graph is a type of mixed graph to provide a graphical representation for the result of marginalizing one or more vertices in a graphical model that takes the form of a directed acyclic graph.
Multigraphs and multidigraphs also support the notion of graph labeling, in a similar way. However there is no unity in terminology in this case. The definitions of labeled multigraphs and labeled multidigraphs are similar, and we define only the latter ones here. Definition 1: A labeled multidigraph is a labeled graph with labeled arcs.
The first published English grammar was a Pamphlet for Grammar of 1586, written by William Bullokar with the stated goal of demonstrating that English was just as rule-based as Latin. Bullokar's grammar was faithfully modeled on William Lily's Latin grammar, Rudimenta Grammatices (1534), used in English schools at that time, having been ...
Graph (discrete mathematics), a structure made of vertices and edges Graph theory, the study of such graphs and their properties; Graph (topology), a topological space resembling a graph in the sense of discrete mathematics; Graph of a function; Graph of a relation; Graph paper; Chart, a means of representing data (also called a graph)
In graph theory, two graphs and ′ are homeomorphic if there is a graph isomorphism from some subdivision of to some subdivision of ′.If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are homeomorphic in the ...