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. B

    Physics Graph question -- Pushing a block on a frictionless surface

    The diagram shows how a force along the x-axis varies with location. A block of mass 7.20 kg moves along the x-axis on a horizontal frictionless surface, influenced by this force. (Graph is attached) A) How much work is done by the force as the block moves from the origin to 8.0 m? B) If the...
  2. metapuff

    Possible Number of Vertices for Graphs with Three Edge Connections

    I want to create graphs where each vertex has three edges, and is connected by these three edges to three distinct vertices. I'd like to know the number of vertices for which this is possible. By playing around a bit, I've found that it's possible for graphs with 4, 8, and 12 vertices. If v is...
  3. K

    Acceleration versus time graph

    when we throw an object upwards its accelaration is negative and after it reaches the maximum height it comes back to us and during that period it has its accelaration still pointing toward the earth. so does that mean that when we draw a accn time graph, for a body thrown up reaching maximum...
  4. E

    Proper way to graph xy = 1 for a cylindrical shell problem

    Homework Statement Proper way to graph xy = 1 for a Cylindrical Shell problems. Homework Equations V = ∫^b_a 2πy f(y) dy The Attempt at a Solution I am rotating around the x-axis, so I am integrating with respect to y, but should I choose x = 1/y, or y = 1/x to solve my problem? How are...
  5. TheExibo

    Need to determine function based on graph

    There is this graph: http://i.imgur.com/BdwhN3b.jpg where the equation of the function must be determined. Down below is some thinking I've done, where I've found that the oblique asymptote is -0.5x+2, and the v-asymptote=6. I know how to solve something similar with 2 x-int's, but I'm having...
  6. D

    MHB Curvature of a graph at a point

    Consider the curve which is graph of a smooth function f : (a,b) → R. Show that at any {x}_{0}\:s.t\:{x}_{0} ∈ (a,b) the curvature is \frac{{f}^{''}({x}_{0})}{{(1+{{f}^{'}({x}_{0})}^{2})}^{3/2}}.
  7. N

    The graph of an exponential function given by f (x) = A(b^x)+c

    Homework Statement The graph goes through the points (-2, 13) and (0, 5) and has the horizontal asymptote y = 4. f(−2) = ____ therefore: ____(B^____ ) = ____ b = The Attempt at a Solution f(−2) = 13 therefore: 1 (B^-2 ) = 13 b = ? not sure Thank you
  8. T

    Given acceleration graph, determine v vs. t and x vs. t graph?

    Homework Statement The title, and assume that t=0, x=0 and v=0. Homework Equations Kinematic equations, and area of triangle and rectangle. The Attempt at a Solution I see what I did wrong with the part that is circled "parabola", as it should be just a straight line, but I am lost as to...
  9. teetar

    How to Find Velocity-Time Graph from Position-Time Graph?

    Homework Statement Not too necessary to follow this format, but here is my question: I know I probably shouldn't ask such a simple question, but how do I find a velocity-time graph from a position-time graph? I know it's just slope, but I'm looking at a curve, and I don't want to differentiate...
  10. T

    Simple Pendulum: The gradient of the graph of T^2 against length

    I've been asked to investigate the value of g. My graph shows that the gradient is around 4.4 as when the length was 0.27m, the squared time period was 1.18s (since this is a T2 against L graph). My question is, of course, why? If I am detecting g, which is 9.81 on earth, why did I get such...
  11. D

    Displacement vs time graph for a given equation of acceleration

    Homework Statement The accompanying graph of position x versus time t represents the motion of a particle. If p and q are both positive constants, the expression that best describes the acceleration a of the particle is Homework Equations (A) a = – - p – - qt (B) a = - –p + qt (C) a = p + qt...
  12. P

    Can Graph Theory Predict Fossil Locations in Research?

    Im not entirely sure what section of PF this post should be in so I apologize in advance if this is not in the correct section. I don't know that much graph theory or the various fields that it can be applied to, but I do know that graph theory can be used in social media etc by using dynamic...
  13. V

    How do I linearize a square root graph?

    Homework Statement These are the Points. X values: 0, 1.98, 3.96, 5.94, 7.92, 9.9 Y values: 1.98, 7.13, 9.08, 11.04, 12.57, 14.51 I need to find the original equation and the linear equation. I can't seem to find the line for square root graphs. 2. The attempt at a solution I know it's a...
  14. T

    MHB Application to graph plots and download or copy them

    Is there an application to graph plots then download or copy the image?Thanks, Tim
  15. K

    How to graph velocity where there is a change in acceleration

    The speed is a constant of 20m/s for 100m (moving on a straight line) after 100m, the car stops at a constant 6m/s/s. *So in this case, speed is equal to velocity? *How do you graph velocity vs time graph and acceleration vs time graph?
  16. I

    MHB Where Can I Find Four Points on an Elliptic Paraboloid Graph?

    graph the elliptic paraboloid $4x^2+y^2-z=0$. find four distinct points on the graph this is the graph. do i just find four random points now that lay on it?
  17. joema

    Polar graph for engine balance on common types?

    In a late 1980s trade journal, I saw a full-page of polar balance diagrams for each major engine type. For each engine type (V6, V8, inline 6, inline 4, V12, etc) a circular polar chart was presented with overlaid color-coded graphs showing 1st, 2nd and 3rd order balance for 360 degrees of...
  18. S

    Finding acceleration on a position-time graph

    The graph below shows a plot of the position of a particle as a function of time. I need help determining whether the statements concerning the motion of the particle are true or false. The graph: http://imgur.com/yNeHoF3 ? - The instantaneous acceleration at B is zero. True - The...
  19. L

    Velocity versus Time graph help?

    My physics lab is using a Motion Detector, to measure the time it takes for a high frequency pulse to travel from the detector to an object and back. I have several questions about Velocity vs Time: What does a horizontal line (with 0 velocity) mean? Does that mean to walk backwards, walk...
  20. L

    Velocity versus Time Graph help?

    What does a vertical line graph pointing straight up mean? Same for down? What does a horizontal line mean? y axis=velocity (m/s) x axis=time (s)
  21. B3NR4Y

    Solve for mass using a graph of a collision

    Homework Statement A 1-kg standard cart collides with a cart A of unknown inertia. Both carts appear to be rolling with significant wheel friction because their velocities change with time as shown in. What is the mass of cart A? The graph below should be used to solve for the mass...
  22. D

    Find Minimum Acceleration from Graph

    So this looks really easy, but I can't get the right answer. It asks you to find the minimum acceleration from the graph: http://s22.postimg.org/f5dutd5ap/pic.png. This is of course the point where the slope is the smallest, and this is from t = 3-4 s or t = 4-5 s, depending on whether you want...
  23. E

    MHB A possible graph for this function?

    I'm not sure how to draw the graph for this question. Could someone please point me in the right direction? I'm also not really sure how you'd find the parent function for the situation. Here's the question: 1) Each of the following situations involve a parent function whose graph has been...
  24. M

    How to graph parametric equations?

    Hi, so after doing some calculus for projectile motion with air resistance, I obtained two equations of vx(t) and vy(t) that describes the vertical and horizontal motion of the projectile. Please tell me if I'm wrong, but I believe since both vx and vy are functions of t, can't they be...
  25. I

    MHB Graph $r(t)$ for t = $\pi/4$: Position and Tangent Vectors

    $r(t)=sin(t)$i $+ 2cos(t)$j $t= \pi/4$ sketch the position vector and the tangent vector $r'(t)=cos(t)$i $- 2sin(t)$j $r(\pi/4)= \frac{\sqrt{2}}{2}$i $+ \sqrt{2}$j $r'(\pi/4)= \frac{\sqrt{2}}{2}$i $- \sqrt{2}$j $\left\langle \frac{\sqrt{2}}{2}, \sqrt{2} \right\rangle$ $\left\langle...
  26. C

    Face Chromatic Number of A Graph

    Hi What is the face chromatic number for the Graph Below? Thank You
  27. C

    Dominating Trail in a Graph

    In the picture below, the "abcdbea" trail is a dominating trail in the graph. My question is that the "agcdbea" is also a dominating trail or NOT? If not why? Thank you ;)
  28. T

    Sine Graph Help: Calculating Uoutput & Drawing Graph

    Homework Statement TASK So I have this task with opamp and I have Uinput Sine Graph, now I have to calculate Uoutput and write it as sine function and draw the sine graph. I know that this is an inverting OPAMP which means that output signal will be inverted, so I just have to flip this...
  29. H

    When scientists use a log graph, do they actually convert x/y w/ log?

    Homework Statement For example, a linear plot would with x and y values would just plot normally where x and y increases linearly from 0 to infinity. When we use a log graph, do we just plug in x and y to a graph in which the x and y go from 0, 10, 100, 1000, or do we convert the numbers...
  30. S

    Velocity versus distance graph

    Homework Statement the velocity of a particle moving along x-axis varies with its position x as shown in figure. The acceleration of a particle varies with position as !
  31. G

    Determine function from the graph

    How to determine the function from its graph if it has a non-simple shape? Given a graph (see attachment) where set of coordinates of any point is known. Are there any techniques to find an equation of the function? So far i can guess, that i need to measure the derivative at multiple points...
  32. S

    Geomertical optics- derivation of graph of (u+v) against u

    Homework Statement may i know how to derive the the sha[pe of graph and get the point of min (2f , 4f) ? i really have no idea how to get the shape of the graph and the min point. The book give it without any explanation. Homework Equations The Attempt at a Solution
  33. D

    Derivation of graph of v against u

    Homework Statement This is the graph of v against u . i am having problem of getting the shape of graph and getting the point (2f, 2f) . can anyone teach me how to derive it? Homework Equations The Attempt at a Solution sorry. i don't know how to use LATEX. it may be quite...
  34. I

    MHB Comparing 3 Points on a 3D Graph

    excuse my TERRIBLE drawing but roughly, is this drawing a good representation of the points? A(-4,0,-1) B(3,1,-5) C(2,4,6) in my drawing i have the axis as 2, 4, 6 etc
  35. gfd43tg

    Is Depth-First Search Order for Graph Traversal Direction-Agnostic?

    Hello, I drew up this graph to try and understand the concept of depth-first search. Starting at node C, I was wondering if its correct for the order to be C-A-B-D or C-B-A-D? It seems like you can traverse in either direction without a problem.
  36. C

    Finding the Mass from an Acceleration vs Force graph

    I have to confirm Newtons 2nd law via a track and trolley experiment Homework Statement The trolley’s mass is kept constant. The weight of the cart (252g) plus two bar weights (500g) is = 752 grams, plus additional weights of either, 10g, 15g, 20g, 25g or 30g for the different trials...
  37. gauss44

    Is this a real graph or is it made up?

    http://ypelletier.wordans.ca/t-shirt/feynman-gildan-homme-man-81965 Is this just a cool design or is it a real physics expression (or something that makes sense)? I figure it might be something like velocity is converted to work and "e-," and work plus "n" equals pressure, or something...
  38. J

    Graphing the Wave Equation with Quadratic Functions

    Homework Statement set \phi = f(x-t)+g(x+t) a) prove that \phisatisfies the wave equation : \frac{\partial^2 \phi}{\partial t^2} = \frac{\partial^2 \phi}{\partial x^2} b) sketch the graph of \phi against t and x if f(x)=x^2 and g(x)=0The Attempt at a Solution part a, I have already gotten the...
  39. I

    Position-Time Graph to Velocity-Time Graph

    Homework Statement Hi everybody. I just started grade 11 physics, and I'm having some serious trouble translating P-T graphs to V-T graphs. I really just can't seem to grasp the concept of this. It also doesn't help that I'm doing an online course and we're not being taught anything. The...
  40. M

    MHB Working out Trend line on a Scatter Graph

    Hi All, Thank you for taking your time to look at my question. I am a web developer and have created a online system that produces graphs but cannot understand how the line of best fit (trend line) is calculated. On paper its easy, just draw it with your hand in between the two lines. But I...
  41. I

    Help with translating a D-T graph into a V-T graph

    Homework Statement Hi. For this assignment, I was told to create a V-T graph with my own values (this doesn't have to make sense in the real world). The assignment says that a ball rolls on the floor, up a ramp, back down the ramp, and backwards along the floor. Here is the diagram...
  42. PhysicsStudnt

    Acceleration - Displacement Graph

    In terms of calculus, How do i prove that the area under the acceleration time graph gives me the change in KE / mass... Attempt at solution... Area under the graph of a function y = f(x) is given by ∫y dx Therefore area under acceleration displacement graph is ∫a ds (considering the...
  43. X

    Good Books or Free Resources for Geometric Graph Theory

    I've been doing some light reading on Geometric Graph Theory, and it seem interesting to me. However, at the moment I've only managed to find a few Wikipedia articles and one .PDF of lecture notes. I'm looking for something which is more complete, such as a book or a website for example...
  44. Mandelbroth

    LaTeX Constructing Petersen Graph in LaTeX: Troubleshooting

    How would one construct a graph, like the Petersen graph, in LaTeX? Is there a good package to use for it? Edit: I should mention that I'm having trouble using instructions (which are not always consistent) that I'm finding on Google.
  45. Adjoint

    Finding change in speed from x vs t graph

    Homework Statement For a particle moving in one dimension, x vs t graph is given below. At each point state whether speed is increasing, decreasing or not changing. Homework Equations Just the basic relation between position, velocity (first derivative of position) and acceleration (second...
  46. F

    Matching a graph to an experiment

    hi there, i am from France, so excuse my mistakes languagewise, please. We got some long-time tasks in physics because our teacher is away. One of them is really hard. I hope you can help me a little bit. Match the following graph to one of these experiments. Since the graph is very small...
  47. K

    Phase difference of 2 points in a same graph

    Homework Statement since point P is ahead of point O, why the displacement , y , of P shouldn't be Asin(wt + 2pi/(x)) ? Homework Equations The Attempt at a Solution
  48. B

    How Do You Graph the Function f(x) = x - [[x]]?

    How do you graph f(x) = x - [[x]]
  49. T

    Finding the Slope of a Function: A Scientific Approach

    I have to find the slope of the function g(x) = x/(x-2), (3,3) my attempt [(3+h)/((3+h)-2)] - [(3)/(3-2)] \div h got rid of (3+h) and 3 [(1/-2) -(1/-2)] \div h 0/h answer in book is -2
  50. Govind_Balaji

    Find maximum velocity in Acceleration-Time Graph

    Homework Statement Find the maximum velocity of the particle using the graph given.(See attachment) Homework Equations Initial velocity was not given. I assumed it to be 0. In book, the solution was 55m/s^2 The Attempt at a Solution Initial acceleration was ##10m/s^2##. Final acceleration...
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