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
