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A drawing of a graph. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines ).
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 [1] laid the foundations of graph theory and prefigured the idea of topology.
Total graph. Tree (graph theory). Trellis (graph) Turán graph. Ultrahomogeneous graph. Vertex-transitive graph. Visibility graph. Museum guard problem. Wheel graph.
Component (graph theory) In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the ...
Graph isomorphism. In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H. such that any two vertices u and v of G are adjacent in G if and only if and are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism ...
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H . Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a ...
Theoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation . It is difficult to circumscribe the theoretical areas precisely. The ACM 's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: [ 1] TCS ...
In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a program during its execution. The control-flow graph was discovered by Frances E. Allen , [ 1 ] who noted that Reese T. Prosser used boolean connectivity matrices for flow analysis before.