graph: Quick Facts

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Illustration of the gas, water, and electricity problem showing three utility buildings labeled W, G, and E, and three houses labeled A, B, and C. Colored lines connect each utility to each house, forming a complete bipartite graph K3,3, with a key identifying water pipes, gas lines, and electrical wires. The diagram demonstrates the non-planar nature of K3,3 in graph theory, as the connections cross over each other.

A graph of the function f(x) = x cubed minus 3x plus 2 is shown on a blue background, with a red curve passing through key points. Local maximum and minimum points are marked with black dots at x equals negative 1 and x equals 1, illustrating important features of the curve.

Five diagrams illustrate types of graphs in mathematics: a simple graph, a multigraph with parallel edges, a complete graph with all possible connections, a graph with a loop, and a directed graph with arrows showing direction.

A geometric diagram of the complete bipartite graph K3,2, showing five vertices with three on one side and two on the other, all connected by curved lines representing edges between each pair of opposite sets.

A geometric diagram illustrating an Eulerian circuit, with arrows tracing a continuous path along intersecting straight lines that form a closed shape connecting five points.

two homeomorphic graphs A and B

two isomorphic graphs and a tree

Examples of linear graphs

A diagram of the complete graph K5, showing five points with every pair connected by straight lines, forming a dense network where several edges cross each other, illustrating its non-planar nature.

Two geometric diagrams compare the complete graphs K4 and K5, showing that K4 can be drawn without edges crossing (planar), while K5 cannot be drawn this way (nonplanar).

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Topics

amphibole quadrilateral directed graph scatter diagram isotope chart tephigram edge path contraction of a graph complete graph audiogram map foundations of mathematics probability and statistics numerals and numeral systems matrix function fractal derivative algorithm vector

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