What is Graph: Definition and 1000 Discussions

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. FritoTaco

    How do I Graph the Sine Function for y=2-sin(2πx/3)?

    Homework Statement Problem: y=2-sin\dfrac{2\pi x}{3} Homework Equations Standard Equation: y = A sin(B(x - C)) + D A: amplitude is A B: period is \dfrac{2\pi}{|b|} C: phase shift is \dfrac{C}{B} D: vertical shift is D Count Formula: \dfrac{1}{4}\cdot period (What you use to choose your...
  2. M

    Concentric Coils EMF from Graph

    Homework Statement Two concentric circular coils of wire lie in a plane. The larger coil has 61 turns and a radius of a = 7.40 cm. The smaller coil has 58 turns and a radius of b = 0.95 cm. The current in the larger coil has a time dependence as shown in the figure. Picture and graph...
  3. M

    MHB Is this theory regarding the graph and the square root valid?

    http://mathhelpboards.com/pre-algebra-algebra-2/find-value-squareroot-3-using-graph-drawing-suitable-straight-line-19973.html I guess I found a method to obtain the square root of any number using the above graph. $x^2-2x-3$ What I did to find the square root of 3 was replace $x^2$ with the...
  4. P

    B What is the formula for the length of the graph of e^x in the first quadrant?

    Hi. I derived a formula for the length of the graph of e^x in the first quadrant between x=a and x=b. It is: sqrt(1+e^(2b)) - sqrt(1+e^(2a)) + (a-b) + log [(sqrt(1+e^(2b)) - 1) / (sqrt(1+e^(2a)) - 1)] I think it works because it gave a value of approx 2.003 units for a=0 and b=1. For a=0 and...
  5. M

    MHB Find Value of Squareroot of 3: Using the Graph & Quadratic Equation

    There is a graph in the form of $x^2-2x-3$ determine the value of $\sqrt{3}$ to the nearest decimal place by drawing an a suitable straight line What must be that straight line ? Usually these kind of problems are solved using the quadratic equation Many thanks :)
  6. N

    MHB What is the area bounded by y = 8 – 2x - x^2 and the x-axis?

    Calculate the area of the region bounded by the graph of the function y = 8 – 2x - x^2 and the x-axis Y = 8 - 2- x^2 0 = 8 – 2 – x^2 (-x – 4)(x – 2) - x – 4 = 0 and x – 2 = 0 -x = 4 x = 2 X = - 4 Do I do this? Y = 8 -2x -x^2 = 8x - (2x^2)/2 - x^3/3 = 8 -...
  7. E

    MATLAB Plotting graph 3D minimization

    Hi to everyone, I'm trying to plot a 3D graph on MATLAB but I do not know how. The function that I want to plot is: y=fminbnd(@(x) wei(x,shape,scale,tw,tf),x0,x1). I would like to plot the minimization of the function wei (y) in function of the shape and the scale. Wei is a function that I...
  8. T

    Find the phase difference of two oscilliators given a graph

    Homework Statement The two oscillators each have the same mass. Use Fig. 4.1 to determine (i) the phase difference between the two oscillators (picture attached) Homework Equations Subtracting to find the horizontal shift The Attempt at a Solution I found the two points where both graphs...
  9. M

    MHB Calculate Brick Velocity & Draw Displacement-Time Graph

    Calculate the velocity of the brick at the bottom of the inclined plane. State the assumption you made for your calculation in part above. & Sketch the displacement-time graph relevant to the movement of the brick along the smooth gutter. (Assume that the brick started to move from the state...
  10. Sade

    Problem Involving work, velocity, given Graph

    Homework Statement An 8kg object is moving in the positive direction of an x axis. When it passes through x=0, a constant force directed along the axis begins to act on it. The figure gives it's kinetic energy K versus position z as it moves from x=00 to x=5.0 ; K(initial)= 30 . The forces...
  11. Stephanus

    B Learning Integrals with the Graph of y=x^2

    Dear PF Forum, I'd like to study integral. But I just realize that I'm lack of basic integral. Can I ask here? Let y=x2 Here is the graph. So, 1. dx is the distance between the red vertical lines? But it's very, very, very small distance. 2. f(x) * dx is the yellow area? 3. ##\int_0^2...
  12. Meerio

    I By what formula is this graph predicted? Cumulative Periastron Time Shift

    I'm confused about how the predictions of this graph were formed. I have this formula: But the change in frequency per second is about : 2x 10^-12 which has a problem because when you multiply this by 10 years you don't even get a change of frequency of 1/1000 of a second and in the graph it...
  13. kelvin490

    MATLAB How to extract data from existing JPEG/TiFF graph?

    Is there any method to extract data from a graph in JPEG/TIFF format, using simple software such as MATLAB? I have a graph as shown below: I only have this picture but no raw data and I want to plot the black curve in this graph. How to get approximate numerical data of the x and y axis...
  14. Dong Aleta

    Can someone identify what this graph is used for?

    Hi, I was asked by my senior to find out what this graph is and how to use it. No details were given as to where they found it. I know already that this is used to compare CSTRs and PFRs performance for first order reactions, but I can't deduce what the expressions Dd/(vxL) and kL/vx are for...
  15. J

    Finding work by Force over Position graph

    Homework Statement An object of 5 kg is acted on by a force and moved from 0.5 to 2.0m. How much work does the force do? As the object moved, friction with a coefficient of 0.2 also acted upon it. What is its final speed if it started at rest? Homework EquationsThe Attempt at a Solution So...
  16. K

    Tangent to Hyperbolic functions graph

    Homework Statement Show that the tangent to ##x^2-y^2=1## at points ##x_1=\cosh (u)## and ##y_1=\sinh(u)## cuts the x-axis at ##{\rm sech(u)}## and the y-axis at ##{\rm -csch(u)}##. Homework Equations Hyperbolic sine: ##\sinh (u)=\frac{1}{2}(e^u-e^{-u})## Hyperbolic...
  17. K

    Tangent to Hyperbolic function graph

    Show that the tangent to ##x^2-y^2=1## at points ##x_1=\cosh (u)## and ##y_1=\sinh(u)## cuts the x-axis at ##{\rm sech(u)}## and the y-axis at ##{\rm -csch(u)}##. $$2x-2yy'=0~\rightarrow~\frac{x}{y}=y'=\frac{\cosh (u)}{\sinh (u)}=\frac{e^u+e^{-u}}{e^u-e^{-u}}$$ The equation...
  18. C

    Graph of bending moment doesn't return to 0

    Homework Statement I gt VA and VB = 85 N and 65 N respectively ... but , my bending moment diagram doesn't return to 0 ... Is there something wrong with the question ? Homework EquationsThe Attempt at a Solution I found that if i didnt include both the moment of 75(0.05) = 3.75Nm , the...
  19. J

    Reading a Potential Energy Graph

    Homework Statement A conservative force F(x) acts on a 2.0 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is graphed in the figure. When the particle is at x = 2.0 m, its velocity is –1.2 m/s. (a) What isF(x) at this position, including sign? Between what...
  20. O

    X ray crystallography - interpreting my graph

    Homework Statement I am currently part way through a laboratory experiment that utilises basic crystallography to ultimately calculate lattice constants and structure factors for NaCl (we receive formal training in the next academic year via full treatment of von Laue, Bragg diffraction etc). I...
  21. A

    Making a graph of CuSO4 concentration vs volume of solution

    Homework Statement Hi, I don't even know where to begin with this type of graph. It does say that the graph should be a straight line. This is for one of my questions for my lab that I am completing. This is the link of mytable with info...
  22. moenste

    Moving-coil galvanometer graph

    Homework Statement A square coil of side a and consisting of N turns is free to rotate about a vertical axis through the mid-points of two opposite sides. It is situated in a uniform horizontal magnetic field of flux density B so that the plane of the coil makes an angle θ with the field. Draw...
  23. Leonardo Machado

    How do I create a logarithmic scale graph and determine line spacing?

    Hello every one. Today's question is: if I'm writte a graph using logarithm scale, must i use the dimensions of the graph "logarithmized" too ? i.e : A Distance x Force graph must have its dimensions as log (m) x log (N) ? or it is just valid for the module ? Thanks for the tips
  24. Meerio

    B Need an explanation for the chances in this graph

    In the paper Advanced LIGO they published some figures with chances. I would like to know how they know that there's a 90% chance for something to be in a specific value. https://dcc.ligo.org/public/0122/P1500218/014/PhysRevLett.116.241102.pdf paper here also have some other questions: What...
  25. M

    MHB How do I plot a distance-time graph using TikZ?

    Problem Plot the above given information in a Distance time graph. Where do I need help Hoping my graph is correct Show that the speed in the final 6 seconds is twice the speed in first 6 seconds But I'm having trouble here , I know $ distance=\frac{distance}{time} $ Many Thanks :)
  26. F

    I Constructing dimensions out of a graph structure?

    I have a question to anyone experienced with graphs and topology. The question is relevant for this topic: https://www.physicsforums.com/threads/a-graph-based-model-of-physics-without-dimensions.887694/ Is it possible to construct an arbitrarily large graph (a set of vertices, a set of edges)...
  27. S

    A Displacement graph of an orbiting body

    If I were to draw a displacement time graph of an arm rotating around it's origin at a constant radius meaning it is a constant displacement from the origin. Meaning the graph looks the same as one of an item that is not moving,how would you draw the displacement time graph of something moving...
  28. K

    MHB Which Quadrant Contains No Solutions to This System of Inequalities?

    If the system of inequalities y ≥ 2x + 1 and y> x/2-1 is graphed in the xy-plane above, which quadrant contains no solutions to the system? A) Quadrant II B) Quadrant III C) Quadrant IV D) There are solutions in all four quadrants. I thing the answer is D . But book says that it is C. I...
  29. R

    Solving exponential equation (using a graph)

    Homework Statement Using experimental data, I am trying to solve the following equation for ##T_2## $$M(t)=M_0 e^{-t/T_2}. \tag{1}$$ Here ##M_0## denotes the initial value. There were 8 data points collected for ##t## and ##M(t).## Here is the resulting graph: The data and equation (1)...
  30. R

    Acceleration vs. Time graph confusion

    Homework Statement This HW is a continuation of the previous lab work we did involving, rings,spring scales and weights. The three hypothesis the groups came to were: 1.The ring will move in the direction of the interaction and will slow down. 2.The ring will move in the direction of the...
  31. C

    Postion vs time graph without time or initial speed?

    Homework Statement Consider the system shown to the right. Particles 1 and 2 are fixed in place while particle three is placed at the location shown and released. Let’s look at the mechanics of q3, which has a mass of 3.00 X 10-5 kg. What will be the net force on q3?What will be q3’s...
  32. toforfiltum

    Equation of ellipsoid and graph

    Homework Statement Equation of ellipsoid is: ##\frac{x^2}{4} + \frac{y^2}{9} + z^2 = 1## First part of the question, they asked to graph the equation. I have a question about this, I know that ##-1\leq z \leq 1##. So what happens when the constant 1 gets smaller after minusing some value of...
  33. toforfiltum

    Finding functions that are a level set and a graph

    Homework Statement This problem concerns the surface determined by the graph of the equation ##x^2 + xy -xz = 2## a) Find a function ##F(x,y,z)## of three variables so that this surface may be considered to be a level set of F. b) Find a function ##f(x,y)## of two variables so that this...
  34. H

    MHB Graph of function intersects line

    Explain why the graph of the function g (x) = x^3 - 2x + 1 intersects the line y = x in each of the intervals (-2, -1), (0, 1) and (1, 2). i hope someone can help me with this. To be honest i do not even know where to start. i sketched g(x) and y=x and i don't see them intersect in the...
  35. Buckethead

    B Graph of rotation curve of a cluster (not a galaxy)

    I'm familiar with galactic rotational curves and there are plenty of graphs depicting such curves, but I'm interested in the rotation curves of entire galactic clusters at the moment and I'm not too good with sifting through what shows up in the search engines. (not a physicist, just a...
  36. B

    I What is the function of this graph?

    I need to create a non linear function from a list of points. I tried creating a 3rd order polynomial trendline on excel but it was a very poor fit. Can anyone give me tips/advice on how to create a function that best fits the following data? Here's what the graph looks like: Here are the...
  37. E

    How to graph amplitude vs. frequency for a Low-Pass Filter?

    Homework Statement For my lab class my professor wants us to graph the theoretical amplitude of the output from a low-pass filter vs. frequency. I have the resistance and capacitance that I chose for the RC circuit and a V(in). Is there an equation that I should be able to use to relate these...
  38. P

    Finding Distance from the Origin Given Velocity Graph

    Homework Statement A rocket-powered hockey puck move along a horizontal friction-less table. The figure (link posted below) shows the graphs of vx and vy, the x- and y- components of the puck's velocity. The puck starts at the origin. How far from the origin is the puck at 4 seconds? Here is...
  39. B

    Acceleration from x vs. t graph

    Homework Statement Describe how to use the position vs. time graph to determine the numerical value of the particle's acceleration. Homework Equations None, these are Lab questions after we released a cart on a track on an incline. The Attempt at a Solution I know that you can derive the...
  40. M

    MHB Write down the equation of the function corresponding to the graph

    Data A graph in the form of $y=(x-1)^2-6$ Problem Write down the equation of the function corresponding to the graph obtained when the above graph is translated 1 unit in the negative direction of the $x$ axis Workings: - Where do I need help In writing the equation of the funtion.
  41. K

    Does a limit exist on a graph at (-1,0) if the point

    Does a limit exist on a graph at (-1,0) if the point is solid, and has a right sided limit, but there is nothing left of the point? I understand that if the left sided limit and the right sided limit are different then it doesn't exist, but on my graph it shows a line coming from the right...
  42. N

    MHB Graph Equation: x-|x|=y-|y| - Seeking Help

    The equation is x-|x|=y-|y| and I need to make a graph for it. So I thought I should solve it by breaking it down to 4 different equations, which would be - x - x = y - y => 0=0 x - x = y + y => 0=2y => y = 0 x + x = y - y => 2x=0 => x = 0 x + x = y + y => 2x=2y => x = y But this isn't...
  43. RoboNerd

    Question on graphing potential

    Homework Statement Homework Equations I know that potential from a point charge equals kq/r and that potential difference equals - (integral of)(E dot dl) The Attempt at a SolutionI tried to approach this problem using the point charge approach by comparing the relative values of kq/r for...
  44. I

    Create Wave Packet Graph in GLE with Fourier Components

    How to add up some Fourier component for example (cosinus function with different phase) to form a wave packet on GLE? acctually, I don't know there is a such command in GLE to add up Fourier components or not. If there is not, so are there other aplications which can be used to do that, such as...
  45. J

    MHB Two problems: linear distance and directed graph

    1.) Two volumes of an encyclopedia stand side by side, in order, on a shelf. A bookworm starts at page i of Volume I and bores its way in a straight line to the last page of Volume II. Each cover is 1 mm thick, and the first volume is 2/5 as thick as the second volume. The first volume is 40 mm...
  46. ItsAnshumaan

    Graph of trigonometric functions

    This is not a homework question but a general doubt. Suppose we have a function y = pcosx, where 'p' is an arbitrary constant. So my question is how will the graph of this function change with different values of 'p'? This doubt can also be extended for other functions like y = pex, y = p...
  47. J

    Design of nonlinear spring from load deflection graph

    Hi Could anybody guide me to a software that can be used to design a non linear spring from load deflection characteristics. need it for both extension and compression spring. thanks noor
  48. M

    MHB Find and approximate value square root of 3 using the roots of the graph.

    Using a graph of function $y=3-(x-1)^2$ which has got its negative & positive root s-0.8 and 2.7 respectively, Find an approximate value for $\sqrt{3}$. Any suggestions on how to begin? Should I be using the quadratic formula here? Many Thanks :)
  49. Saracen Rue

    Area enclosed between this graph and the x-axis

    Homework Statement For the relationship ##|y| = cos(x-y), -\frac {π} {2} ≤ x ≤ \frac {π} {2}##, use calculus and algebra to determine the total area enclosed between the graph and and the x-axis. Homework Equations Area between points ##a## and ##b## = ##∫_a^b f(x)dx## given that ##f(x)>0##...
  50. Turbodog66

    Matching Equations to Spheres: Solving the Mystery

    I have been given a problem with 4 equations, that need to be matched up to the corresponding image. I have worked the equations already and determined their center, but for the life of me I cannot seem to figure out which graph goes with which equation. The images are not that easy to read...
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