Fraenkel, Scheinerman, and Ullman show that "'Undirected Vertex Geography "'can be solved in polynomial time, whereas "'Undirected Edge Geography "'is PSPACE-complete, even for planar graphs with maximum degree 3.
12.
The former type of graph is called an " undirected graph " and the edges are called " undirected edges " while the latter type of graph is called a " directed graph " and the edges are called " directed edges ".
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A valid schedule for the disjunctive graph may be obtained by finding an acyclic orientation of the undirected edges that is, deciding for each pair of non-simultaneous tasks which is to be first, without introducing any circular dependencies and then ordering the resulting directed acyclic graph.
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For instance, a Bayesian network represents a system of probabilistic events as vertices in a directed acyclic graph, in which the likelihood of an event may be calculated from the likelihoods of its predecessors in the DAG . In this context, the moral graph of a DAG is the undirected graph created by adding an ( undirected ) edge between all parents of the same vertex ( sometimes called " marrying " ), and then replacing all directed edges by undirected edges.
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For the special case of conjunctive queries in which all relations used are binary, this notion corresponds to the treewidth of the dependency graph of the variables in the query ( i . e ., the graph having the variables of the query as nodes and an undirected edge \ { x, y \ } between two variables if and only if there is an atomic formula R ( x, y ) or R ( y, x ) in the query ) and the conjunctive query is acyclic if and only if its dependency graph is acyclic.
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