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In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
The graph shown here appears as a subgraph of an undirected graph if and only if models the sentence ,,,... In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices, with predicates for equality and adjacency testing.
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).
An early exact algorithm for finding a Hamiltonian cycle on a directed graph was the enumerative algorithm of Martello. [3] A search procedure by Frank Rubin [5] divides the edges of the graph into three classes: those that must be in the path, those that cannot be in the path, and undecided. As the search proceeds, a set of decision rules ...
This notion has made it possible to use the methods of graph theory in universal algebra and several other areas of discrete mathematics and computer science.Graph algebras have been used, for example, in constructions concerning dualities, [2] equational theories, [3] flatness, [4] groupoid rings, [5] topologies, [6] varieties, [7] finite-state machines, [8] [9] tree languages and tree ...
Gottlob & Lee (2007) observed that Courcelle's theorem applies to several problems of finding minimum multi-way cuts in a graph, when the structure formed by the graph and the set of cut pairs has bounded treewidth. As a result they obtain a fixed-parameter tractable algorithm for these problems, parameterized by a single parameter, treewidth ...
A minor of an undirected graph G is any graph that may be obtained from G by a sequence of zero or more contractions of edges of G and deletions of edges and vertices of G.The minor relationship forms a partial order on the set of all distinct finite undirected graphs, as it obeys the three axioms of partial orders: it is reflexive (every graph is a minor of itself), transitive (a minor of a ...