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Switching {X,Y} in a graph. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs.. Switching a set of vertices in a (simple) graph means reversing the adjacencies of each pair of vertices, one in the set and the other not in the set: thus the edge set is changed so that an adjacent pair becomes nonadjacent and a nonadjacent ...
Clique-sums are important in graph structure theory, where they are used to characterize certain families of graphs as the graphs formed by clique-sums of simpler graphs. The first result of this type [2] was a theorem of Wagner (1937), who proved that the graphs that do not have a five-vertex complete graph as a minor are the 3-clique-sums of ...
Every flag complex is a clique complex: given a flag complex, define a graph G on the set of all vertices, where two vertices u,v are adjacent in G iff {u,v} is in the complex (this graph is called the 1-skeleton of the complex). By definition of a flag complex, every set of vertices that are pairwise-connected, is in the complex.
A graph isomorphism is a one-to-one incidence preserving correspondence of the vertices and edges of one graph to the vertices and edges of another graph. Two graphs related in this way are said to be isomorphic. isoperimetric See expansion. isthmus Synonym for bridge, in the sense of an edge whose removal disconnects the graph.
In graph theory, two graphs and ′ are homeomorphic if there is a graph isomorphism from some subdivision of to some subdivision of ′.If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are homeomorphic in the ...
Subgraph isomorphism is a generalization of the graph isomorphism problem, which asks whether G is isomorphic to H: the answer to the graph isomorphism problem is true if and only if G and H both have the same numbers of vertices and edges and the subgraph isomorphism problem for G and H is true. However the complexity-theoretic status of graph ...
The prostate, a.k.a. the "male G-spot," can produce mind-blowing orgasms. Sex experts explain where it is, how to stimulate it, and more.
A planar graph and its dual. Every cycle in the blue graph is a minimal cut in the red graph, and vice versa, so the two graphs are algebraic duals and have dual graphic matroids. In mathematics, Whitney's planarity criterion is a matroid-theoretic characterization of planar graphs, named after Hassler Whitney. [1]