Graphs Definition and 655 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. f95toli

    Software for creating graphs for presentations

    I was wondering if anyone has a suggestion for software that can be used to create good looking graphs for e.g Powerpoint presentations? | have access to a range of packages (Excel, Origin, Matlab) but none of them can create really "slick" locking graphs (but they are fine for figures in...
  2. M

    Explanation of graphs involving capacitors (charging/discharging)

    Homework Statement I've tested the circuit above, when the switch is in the 2nd position (not the one on the picture) and got the below graph from the plotted data I received. The capacitor C1 has been charged to 4V, and will start to discharge through R3. I'll have to explain...
  3. S

    MHB Sketching graphs in polar coordinates

    I don't understand why I am screwing this up so bad. Sketch the graph of the equation r = 2 + 4cos(\theta) in polar coordinates. So I did: 0 = 2 + 4cos(\theta) = -\frac{1}{2} = cos(\theta) Then got cos(\theta) is -\frac{1}{2} @ \frac{2\pi}{3} and @ \frac{4\pi}{3} Then i plotted points to...
  4. datafiend

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  5. G

    Reviewing manuscript for labmate, and they use truncated bar graphs

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  6. sbstratos79

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  7. T

    Difference between graphs of -f(x) and f(-x)

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  8. G

    Control Systems Engineering - Signal Flow Graphs

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  9. G

    Irreducible graphs and srednicki's book

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  10. A

    MHB Why Do Class 1 Graphs Contain More Graphs Than Class 2?

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  11. C

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  12. E

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  13. S

    MATLAB How to plot 3d graphs from multiple .dat files in matlab?

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  14. C

    MHB Graphs of Negative Fractional Powers x^(-p/q)

    Can someone explain how these graphs are drawn. How does the value of p/q affect this graph? How does the domain and range change? How are the asymptotes found? The below is an image about what I'm talking about: Here is a question the deals with this type of graph (no idea how to solve it...
  15. C

    MHB Graphs of Functions with fractional powers x^(p/q)

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  16. M

    MHB Exercise about connected graphs

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  17. S

    [Discrete math] Finding simple, nonisomorphic graphs with 4 nodes

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  18. T

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  19. LarryS

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  20. jk22

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  21. 1

    How to draw graphs and level curves?

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  22. 1

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  23. P

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  24. F

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  25. N

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  26. O

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  27. N

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  28. J

    How to Set Up Integrals for Volumes by Rotation Involving Arctan and Arcsin?

    Homework Statement Set up the integral (but do not solve) for the volume of the object created by rotating the region bounded by y = arctan(x) and y = arcsin(x) in the first quadrant. Homework Equations I = ∏∫(f(x)^2 - g(x)^2) dx The Attempt at a Solution a.) rotate about he x...
  29. A

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    I understand how position vs. time diagrams can give velocity. If the line is flat then the velocity is zero (the particle is still), and all the other basic things I need to know, but what if the line was vertical? The slope would be undefined; therefore, velocity would be undefined. In...
  30. X

    Graphs of Fractional Functions

    Hello, I have a problem that has me stumped, please help. Question: Find the equations of the asymptotes of the following fractional functions., and then, draw the graph and label x- and y-axis points of intersection. The equation: y= x/(x + 1) My try at it: I first divided x by (x + 1) to get...
  31. D

    Engineering How to plot output graphs of circuits involving diodes and capacitors?

    Homework Statement Given that the diodes are ideal for the circuits a) and b), plot each of their output for the input shown. Label the most positive and most negative levels. Assume CR >> THomework Equations The Attempt at a Solution I am having a really hard time understanding the role of...
  32. mathmaniac1

    MHB Position time graphs for different acceleration

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  33. Fernando Revilla

    MHB Symmetric Graphs: f(x)=3^x and g(x)=(1/3)^x Explained

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  34. P

    Polar graphs really important and tangents

    Hi, I really need help with this as exam is tomorrow The question is to find the points on the cardioid r=a(1+costheta) where the tangents are perpendicular to the initial line here is the answer http://gyazo.com/e8b4cbd36f0ef71d0cdf13be256d8618 Why is pi not included in the...
  35. S

    I'm trying to create a function that graphs a capital B

    I'm trying to create a function that graphs a capital "B" So it's not really a function, it has multiple y values for some x values, but I'm achieving that by using "±" signs when appropriate. My problem, however is the vertical line. I thought for a long time how to come up with a equation...
  36. P

    Why Plot T² Against 1/K for a Straight Line Graph in Oscillation Studies?

    So, I have to assess the relationship between the Constant of a Spring and the Time Period of Oscillations. I have researched the equation that links the two and I know that to have a straight line graph I need to plot: T2 against 1/K However, I do not know why; how I get to that conclusion...
  37. O

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    Homework Statement For the conic, 5x2+4xy+5y2=9, find the direction of the principal axes, sketch the curve. I found the eigenvalues as 3,7 but have no idea whether the 'new' equation is 3(x')2+7(y')2 or 7(x')2+3(y')2 is there a way to determine which 'way' it goes? I took a guess...
  38. P

    Sketching Graphs using limit information

    Homework Statement For each of the four cases below, sketch a graph of a function that satisfies the stated conditions. In each case, the domain of the function should be all real numbers. (professor also mentioned he wants us to write it out in piecemeal function format) a) lim(x→2) of...
  39. I

    Area Under Graphs: Finding Work Done

    Okay, so I've got a question on graphs and areas under curves. For example, a force-distance graph, with force on the y-axis and distance on the x-axis, where you find work done from that graph. I understand that a constant force will produce a horizontal line on the graph, like so: Force...
  40. M

    MHB Polar Graphs and a question about their poles

    Trying to help someone out with their assignments on basic polar graphs. This first question is very easy to determine the poles from as the limacon has an inner loop. But when you have a limacon WITHOUT (below) an inner loop, how does the "max from pole" and "min from pole" figure? It's been...
  41. K

    Graphs of Frequency for Car Moving in a Circle

    Homework Statement A car with a horn making a frequency of 'f' Hz is driven in a circle with a radius of 'r' m. The uniform velocity of the car is v ms-1. Draw graphs showing the frequency observes by the observer who is standing on; a) Position A b) Position B (Position B is very far...
  42. M

    Sketch the graphs of the functions - Calculus question

    Homework Statement Sketch the graphs of the functions. Indicate intervals on which the function is increasing, decreasing, concave up, or concave down; indicate relative maximum points, relative minimum points, points of inflection, horizontal asympototes, vertical asymptotes, symmetry, and...
  43. M

    Sketch the graphs of the functions - Calculus question

    Homework Statement Sketch the graphs of the functions. Indicate intervals on which the function is increasing, decreasing, concave up, or concave down; indicate relative maximum points, relative minimum points, points of inflection, horizontal asymptotes, vertical asymptotes, symmetry, and...
  44. P

    Refractive index experiment/finding error on graphs

    I'm writing a physics practical report on the refractive index of glass. We performed an experiment in which we measured the incident angle and the refractive angle of light entering a glass block. When plotting sin(ϴa) against sin(ϴg) with the y-intercept as 0 (to satisfy snell's law...
  45. L

    LaTeX How to Fit Graphs and Text on the Same Page in LaTeX?

    There was not enough room to fit my graphs in the text where they were supposed to go so latex put them in the next page. This meant that this page only has these two graphs and the text begins again on the page after that. There is a lot of space between (see attached). How do i make it take up...
  46. R

    Force and Potential Energy Graphs: Mastering Physics HW 11.39

    Homework Statement The figure below shows the force exerted on a particle that moves along the x-axis. Draw a graph of the particle's potential energy as a function of position from x=0 to x=1.1 . Let U be zero at x=0.Homework Equations F=-dU/dxThe Attempt at a Solution I decided to divide the...
  47. B

    Carnot Cycle Graphs: Understand Work and Temperature

    Hello, In the Volume vs. pressure graph I understand the area under the curve is work. However, I have a hard time reconciling this graph with a pressure vs. temperature or a temperature vs. volume graph. What does the area inside the box represent? Work? Like which parts on the P vs. V graph...
  48. B

    MHB Nonisomorphic graphs with 10 vertices all of degree 3

    Hello, I need help finding all non-isomorphic graphs that have exactly ten vertices, and each vertex has degree three. Does anyone know where I could find them? Or how many there are? I know that playing around with generalized Petersen graphs gives a few, but I doubt that would give all of...
  49. R

    The slopes of these graphs represent what? (Magnetic Fields)

    For a magnetic fields lab I am asked to graph the data and from there, use the slope to find a certain value. For one of them, I am asked to plot the current (x) vs the magnetic field (y). The slope is supposed to give me a value, I have the slope, no clue what the value would represent...
  50. B

    Graphs of Continuous Functions and the Subspace Topology

    Let U be a subset of ℝn be an open subset and let f:U→ℝk be a continuous function. the graph of f is the subset ℝn × ℝk defined by G(f) = {(x,y) in ℝn × ℝk : x in U and y=f(x)} with the subspace topology so I'm really just trying to understand that last part of this definition...
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