Graph Definition and 999 Threads

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points.
Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection.
Plane graphs can be encoded by combinatorial maps or rotation systems.
An equivalence class of topologically equivalent drawings on the sphere, usually with additional assumptions such as the absence of isthmuses, is called a planar map. Although a plane graph has an external or unbounded face, none of the faces of a planar map has a particular status.
Planar graphs generalize to graphs drawable on a surface of a given genus. In this terminology, planar graphs have genus 0, since the plane (and the sphere) are surfaces of genus 0. See "graph embedding" for other related topics.

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  1. LCSphysicist

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    Sketch a qualitatively accurate graph of the entropy of a substance as a function of temperature, at fixed pressure. Indicate where the substance is solid, liquid, and gas . Explain each feature of the graph briefly. What you think about?: dU = -P*dV + Q*dS (1) V = C*T => dV = C*dT Nfk*dT/2 +...
  2. karush

    MHB Tikz graph of y^3−3y^2−x−x^3+2=0, |x|<1

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  3. F

    I Determining the Equation of a Sine and Cosine Graph that speeds up

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  4. B

    Interpreting Stress-Strain Graph: Which Material Has the Highest Ductility?

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  5. A

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  6. A

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  7. A

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  8. F

    Calculating velocity from the position versus time graph

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  9. SymNeric

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  10. Luke Tan

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  11. ttpp1124

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  12. P

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  13. jaumzaum

    B Learn Special Relativity: Understanding Graphs for X-T System

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  14. B

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  15. il postino

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  16. V

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  17. Z

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  18. IamVector

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  19. karush

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  20. J

    MHB Minimum Degree of a Random Graph (Probabilistic Method)

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  21. J

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  22. U

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  23. adska

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  24. Frigus

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  25. J

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  26. S

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  28. FireAP

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  29. S

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  30. N

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  31. S

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  32. T

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  33. karush

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  34. S

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  35. D

    MHB How to get started in algorithmic graph theory?

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  36. F

    I Classify the isomorphism of a graph

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  37. Johny Boy

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  38. R

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  39. T

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  40. N

    ProProgram for drawing functions

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  41. P

    I Why v vs. t graph signifies but s vs. t^2 doesn't ?

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  42. J

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  43. E

    Quick question about the representation of error on a graph

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  44. R

    Domination number of a graph G

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  45. naushaan

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  46. J

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  47. jisbon

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  48. Like Tony Stark

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  49. Arman777

    Comp Sci Low Pass Filter, plotting a graph

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  50. G

    MHB Value of b, y-intercept of Quadratic graph

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