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nontrivial graph

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  • Graph automorphism — In graph theoretical mathematics, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge vertex connectivity.Formally, an automorphism of a graph G = ( V , E ) is a permutation sigma;… …   Wikipedia

  • Minor (graph theory) — In graph theory, an undirected graph H is called a minor of the graph G if H is isomorphic to a graph that can be obtained by zero or more edge contractions on a subgraph of G. The theory of graph minors began with Wagner s theorem that a graph… …   Wikipedia

  • Cubic graph — Not to be confused with graphs of cubic functions. The Petersen graph is a Cubic graph …   Wikipedia

  • Tietze's graph — The Tietze s graph Vertices 12 Edges 18 Diameter …   Wikipedia

  • Algebraic graph theory — is a branch of mathematics in which algebraic methods are applied to problems about graphs. In one sense, algebraic graph theory studies graphs in connection with linear algebra. Especially, it studies the spectrum of the adjacency matrix, the… …   Wikipedia

  • Bridge (graph theory) — A graph with 6 bridges (highlighted in red) An undirected connected graph with no cut …   Wikipedia

  • Václav Chvátal — Václav (Vašek) Chvátal (born 1946 [http://www.ece.tufts.edu/colloquia/archives/fall00/perfectGraphs.html Biography included with abstract for talk by Chvátal at Tufts Univ., 2000] .] ) (pronounced|ˈvaːt͡slaf ˈxvaːtal) is a professor in the… …   Wikipedia

  • Strongly connected component — Graph with strongly connected components marked A directed graph is called strongly connected if there is a path from each vertex in the graph to every other vertex. In particular, this means paths in each direction; a path from a to b and also a …   Wikipedia

  • Stallings theorem about ends of groups — In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group G has more than one end if and only if the group G admits a nontrivial decomposition as an amalgamated free product or… …   Wikipedia

  • Modular decomposition — In graph theory, the modular decomposition is a decomposition of an undirected graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph. Unlike connected components, however, one module can… …   Wikipedia

  • Bass–Serre theory — is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated… …   Wikipedia

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