Extensions and generalizations of graphs | Families of sets | Algebraic graph theory

Two-graph

In mathematics, a two-graph is a set of (unordered) triples chosen from a finite vertex set X, such that every (unordered) quadruple from X contains an even number of triples of the two-graph. A regular two-graph has the property that every pair of vertices lies in the same number of triples of the two-graph. Two-graphs have been studied because of their connection with equiangular lines and, for regular two-graphs, strongly regular graphs, and also finite groups because many regular two-graphs have interesting automorphism groups. A two-graph is not a graph and should not be confused with other objects called 2-graphs in graph theory, such as 2-regular graphs. (Wikipedia).

Two-graph
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From playlist Graph Theory

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From playlist Graph Theory (Discrete Math)

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From playlist Introduction to Algorithms

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From playlist Graph Theory

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From playlist CSE547 - Discrete Mathematics - 1999 SBU

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From playlist Graph Theory

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From playlist Graph Theory

Related pages

Graph theory | Norm (mathematics) | Eigenvalues and eigenvectors | Regular graph | Seidel adjacency matrix | Automorphism group | Equiangular lines | Mathematics | Strongly regular graph | Signed graph | Gram matrix | Euclidean space | Finite group | Symmetric matrix